tidal sedimentology

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Principles of Tidal Sedimentology


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Richard A. Davis, Jr. Robert W. DalrympleEditors

Principles of TidalSedimentology


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EditorsRichard A. Davis, Jr.Harte Research InstituteTexas A&M UniversityOcean Drive 6300Corpus Christi, TX 78412USA

Coastal Research LaboratoryDepartment of GeologyUniversity of South FloridaTampa, FL [email protected]

Robert W. DalrympleDepartment of Geological Sciences andGeological EngineeringQueens UniversityMiller HallKingston, ON K7L 3N6

[email protected]

ISBN 978-94-007-0122-9 e-ISBN 978-94-007-0123-6DOI 10.1007/978-94-007-0123-6Springer Dordrecht Heidelberg London New York

Library of Congress Control Number: 2011939475

Springer Science+Business Media B.V. 2012No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by anymeans, electronic, mechanical, photocopying, microfilming, recording or otherwise, without writtenpermission from the Publisher, with the exception of any material supplied specifically for the purpose ofbeing entered and executed on a computer system, for exclusive use by the purchaser of the work.

Cover illustration: Fig. 5.13 (upper part) from this book.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)


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v

Tides have fascinated humans for millennia. Their regularity and their apparent

correlation with lunar behavior intrigued natural philosophers, even the Greeks, who

live on an essentially tideless sea although there are strong tidal currents in localized

constrictions. Apparently, they learned about tides from areas outside the Straits of

Gibralter and from the Arabs who experienced significant tides in the Persian Gulf.

From a practical perspective, tidal changes in water elevation and the currents

associated with these changes were of great importance for shipping and militarypurposes. In areas such as the countries surrounding the southern North Sea, such

considerations required accurate tidal predictions, which in turn drew the attention of

some of the greatest astronomers and mathematicians.

Among the notable individuals who devoted at least part of their careers to the

study of tides, and have contributed to our understanding of them are Galileo,

Descartes, Bacon, Kepler, Euler, Laplace, and Lord Kelvin (Cartwight 1999). Indeed,

many of the widely used mathematical techniques that we now take for granted were

developed to help understand the behavior of the tides. More recently, interest in tides

and storm surges has been fostered by the need to protect ever-increasing coastal

population centers from catastrophic inundation, and by the desire to reclaim tidal

flats for agricultural and industrial purposes. Foremost in this activity have been TheNetherlands, Germany, and adjacent parts of Denmark.

Research on the nature of tidal deposits has been underway for about 50 years.

Early studies on the Wadden Sea along the North Sea coast of The Netherlands and

Germany were among the original landmark efforts in this area (e.g. van Straaten

1954; Postma 1961; Reineck 1963), and were followed closely by work in England

(Evans 1965) and France (Bajard 1966). Such efforts were driven by the dual need to

understand the coastal zone for the protection of population centers and to provide an

actualistic analog for ancient sedimentary successions. In North America, Kleins

work on the Bay of Fundy (Klein 1963) initiated detailed efforts in that part of the

world. The early German work in the North Sea had a major biological and ichno-

logical component, a topic that was pursued systematically at the Skidaway Institute

of Oceanography in the southeastern United States (e.g. Frey and Howard 1969).

Despite having some of the most widespread tidal flats in the world, work along the

Chinese coast was relatively slow to develop, although there were notable early studies

(e.g. Wang 1963). In the carbonate realm, pioneering studies were conducted on the

tidal flats of Andros Island, the Bahamas (e.g. Shinn et al. 1969), and the Persian Gulf

(Evans et al. 1969).

In spite of important work on the shallow-marine tidal deposits in the seas of

northwestern Europe (e.g. Stride 1963), most of the early work on modern tidal

Preface


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vi Preface

deposits was devoted to study of intertidal environments, mainly because they were

readily accessible. This fixation on the intertidal zone is perhaps nowhere more

evident in the influential compilation of examples contained in the book Tidal

Deposits: A Casebook of Recent Examples and Fossil Counterparts(Ginsburg 1975).

Indeed, the upward-fining succession developed by the progradation of a tidal flat

was among the very first facies models created. Application of these studies to the

rock record was widespread in the carbonate literature, with numerous documentedexamples being published through the 1960s, 1970s and 1980s. By comparison, the

extension of the work on the modern tidal deposits to ancient siliciclastic successions

was slow. At least one impediment to the widespread application to the ancient was

the notion put forward by Irwin (1965), and since largely disproven, at least for

siliciclastic sediments, that the expansive epicontinental seas of the past were largely

tideless, as a result of frictional damping of the tidal wave. An even greater impedi-

ment was the lack of definitive criteria for the recognition of tidal deposits, given that

exposure indicators are much less easily preserved in siliciclastic tidal deposits than

they are in carbonates. Thus, a milestone in the study of tidal deposits occurred in

1980 with the publication by Visser (1980) of tidal bundles in cross beds formed by

subaqueous dunes, which provided the first documentation of a definitive indicator oftidal sedimentation, spawned the widespread recognition of ancient tidal deposits in

an ever-growing number of localities.

Gradually, the focus of research on modern tidal environments has shifted away

from tidal flats, toward a more comprehensive examination of tidal sedimentation in

a wide range of settings, including even the deep ocean. Studies have tended to become

more holistic in their treatment of entire depositional systems, rather than concentrating

on only one part (e.g. tidal flats) of the whole. This more comprehensive approach is

evident in many of the papers in this volume.

Because of the increasing attention given to tidal deposits it became important to

organize a uniform nomenclature and approach to their study. As a consequence, Robert

N. Ginsburg organized and hosted a conference of interested researchers in February of1973. It included field experiences in both siliciclastic (Sapelo Island, Georgia, USA)

and carbonate areas (Florida Keys, USA and the Bahamas), followed by presentations

of research on tidalites (a term coined by George deVries Klein (1971)) by all in

attendance. The next similar conference was held in The Netherlands in 1986, followed

in regular succession by a series International Conferences on Tidal Sedimentology that

has met in Calgary, Canada (1989), Wilhelmshaven, Germany (1992), Savannah,

Georgia USA (1996), Seoul, Korea (2000), Copenhagen, Denmark (2004) and, most

recently, in Qingdao, China (2008). The next meeting will be in Caen, France in 2012.

The meeting in 2008 in China was particularly stimulating with an attendance that

surpassed any previous meeting. The expansion of interest in tidal deposits appears to

be spurred by two factors: the need to understand coastal tidal environments in order

to predict how these sensitive environments might respond to sea-level rise and

climate change; and providing data and interpretations to help in understanding

ancient depositional environments that were influenced by tides. Davis thought it was

a good time to assemble a principles-type volume on the topic of tidal sedimentology

given that no such synthesis exists, and because there has been so much new research

on tidal environments and deposits over the last few years. Dalrymple agreed to be

co-editor and the result of their efforts is this volume.

The purpose of this volume is to provide the first-ever, high-level overview of tidal

sedimentology. Many of the chapters contain the first-ever synthesis of information


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on the particular topic! The approach is comprehensive with state-of-the-art reviews

of the full spectrum of tidal depositional environments, from supratidal salt marshes,

through the full range of coastal environments and continental shelves, to the deep

sea. Examples from modern environments and ancient deposits are provided, and

both siliciclastic and carbonate environments are discussed. The book is organized in

the following four parts. (1) Chapters 14 provide overviews of the fundamentals of:

the generation of tides, the nature of sediment transport by tidal currents, the criteriaby which tidal deposits can be recognized, and the ichnology of tidal deposits. The

later chapter represents the first time that the ichnological characteristics of tidal depo-

sits have been reviewed systematically. (2) Chapters 514 review the characteristics

of the full range of siliciclastic tidal environments, including both tide-dominated

estuaries and deltas, as well as the various tidal components of barrier-lagoon systems.

These chapters cover all aspects of the sedimentology of these environments, from

the details of the physical processes operating in them, through the morphodynamics

and facies, and the stratigraphic organization of the deposits. (3) Chapters 1518

provide syntheses of particular times and places in earth history where tidal deposits

are particularly notable. The chapter on the Precambrian reviews tidal sedimentation

at a time when the Moon was significantly closer to the Earth and the tide-generatingforce should have been stronger. The reviews of the tidal deposits in the Illinois Basin

(Carboniferous age), Western Interior Seaway (Cretaceous) and Spanish Pyrenean Basin

(Eocene) provide unique insights into the large-scale (tectonic and relative sea level)

controls on the spatial and temporal distribution of tidal sedimentation. (4) Chapters

1921 discuss tidal sedimentation in modern and ancient carbonate environments.

Experts from throughout the world have been chosen to be the lead authors on

each of the chapters. They and their co-authors build on their considerable personal

experience to present insightful syntheses of the latest research in the particular topic.

Each chapter has abundant illustrations, many of which are in color to enhance their

effectiveness. References are extensive and include historically important ones as

well as those on the leading edge of each topic.Because of the uniquely broad coverage within each of the chapters, and in the

volume as a whole, this book should be of value to a wide range of researchers. Workers

who study modern sedimentary environments, and especially coastal settings, including

environmental managers and coastal engineers, will find much about the dynamics of

these environments that will assist them to develop protection strategies that are

compatible with the natural behavior of these complex systems, including their

response to potentially rising sea level. Geologists who study ancient sedimentary

successions, whether for more academic or more applied reasons, will find a wealth

of information about the behavior of tidal environments, ranging from the nature of

the facies, through small-scale sedimentary successions, to the largest-scale sequence-

stratigraphic control on tidal sedimentation.

The editors and authors gratefully acknowledge the financial support of numerous

funding agencies that have provided support for their respective research activities.

They also thank the people who have provided excellent and constructive reviews

(see below). The editors appreciate the cooperation of Dr. Robert Doe and his staff at

Springer Publishers.


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viii Preface

Chapter Reviewers

Clark Alexander

Serge Bern

Sean Bingham

Ron BoydMargie Chan

Kyungsik Choi

Poppe de Boer

Robert Dott

Paul Enos

Jon French

Shu Gao

Murray Gingras

Liviu Giosan

Steven Greb

Gary Hampson

Steve Hasiotis

Christopher Kendall

George Klein

Erik Kvale

Tim Lawton

Don McNeil

Bruce Nocita

Nora Noffke

David PiperPiret Plink-Bjorklund

Brian Pratt

Denise Reed

Joshiki Saito

Gene Shanmugam

Gene Shinn

Ronald Steel

John Suter

S. Temmerman

Bernadette Tessier

Ad van der Spek

Grant Wach

Ping Wang

Colin Woodruff

Paul Wright

References

Bajard J (1966) Figure et structures sdimentaires dans la partie orientale de la baie de MontSaint-Michel. Rev Geog Phys Geol Dyn 8:39112

Cartwright DE (1999) Tides: a scientific history. Cambridge University Press, Cambridge, 292 pEvans G (1965) Intertidal flat sediments and their environments of deposition in The Wash. J Geol

Soc Lond 121:209245Evans G, Schmidt V, Bush P, Nelson H (1969) Stratigraphy and geologic history of the Sabkha,

Persian Gulf. Sedimentology 12:145159Frey RW, Howard JD (1969) A profile of biogenic sedimentary structures in a Holocene barrier

island-salt marsh complex, Georgia. Gulf Coast Assoc Geol Soc Trans 19:427444Ginsburg RN (1956) Environmental relationships of grain size and constituent particles in some

south Florida carbonate sediments. Bull Am Assoc Petrol Geol 40:23842427

Ginsburg RN (1975) Tidal deposits: a casebook of recent examples and fossil counterparts. Springer,New York, 426 p

Irwin ML (1965) General theory of epeiric clear water sedimentation. Bull Am Assoc Petrol Geol49: 445459

Klein deV G (1971) A sedimentary model for determining paleotidal range. Geol Soc Am Bull82:25852592

Postma H (1961) Transport and accumulation of suspended matter in the Dutch Wadden Sea. NethJ Sea Res 1:148190

Reineck H-R (1963) Sedimentgefge im Bereich der sdlichen Nordsee. Abhandl SenckenberNaturforsch Ges 505:1138

Shinn EA, Lloyd RM, Ginsburg RN (1969) Anatomy of a modern carbonate tidal flat, Andros Island,Bahamas. J Sediment Petrol 39:112123


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Stride AH (1963) Current-swept sea floors near the southern half of Great Britain. Q J Geol SocLond 119:175199

van Straaten LMJU (1954) Composition and structure of recent marine sediments in the Netherlands.Leidse Geol Mededel 19:1110

Visser MJ (1980) Neap-spring cycles reflected in Holocene subtidal large-scale bedform deposits: apreliminary note. Geology 8:543546

Wang Y (1963) The coastal dynamic geomorphology of the northern Bohai Bay. In: Wang Y (ed)

Collected oceanic works of Nanjing University. Nanjing University Press, Nanjing (in Chinesewith English abstract)

Corpus Christi, Texas USA

Kingston, Ontario, Canada


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Contents

1 Tidal Constituents of Modern and Ancient

Tidal Rhythmites: Criteria for Recognition and Analyses. . . . . . . . . . 1

Erik P. Kvale

2 Principles of Sediment Transport Applicable

in Tidal Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Ping Wang 3 Tidal Signatures and Their Preservation

Potential in Stratigraphic Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Richard A. Davis, Jr.

4 Tidal Ichnology of Shallow-Water Clastic Settings . . . . . . . . . . . . . . 57

Murray K. Gingras and James A. MacEachern

5 Processes, Morphodynamics,

and Facies of Tide-Dominated Estuaries . . . . . . . . . . . . . . . . . . . . . . . . 79

Robert W. Dalrymple, Duncan A. Mackay,

Aitor A. Ichaso, and Kyungsik S. Choi

6 Stratigraphy of Tide-Dominated Estuaries . . . . . . . . . . . . . . . . . . . . . . 109

Bernadette Tessier

7 Tide-Dominated Deltas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Steven L. Goodbred, Jr. and Yoshiki Saito

8 Salt Marsh Sedimentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Jesper Bartholdy

9 Open-Coast Tidal Flats. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Daidu Fan

10 Siliciclastic Back-Barrier Tidal Flats . . . . . . . . . . . . . . . . . . . . . . . . . . . 231Burghard W. Flemming

11 Tidal Channels on Tidal Flats

and Marshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269

Zoe J. Hughes

12 Morphodynamics and Facies Architecture

of Tidal Inlets and Tidal Deltas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

Duncan FitzGerald, Ilya Buynevich, and Christopher Hein

13 Shallow-Marine Tidal Deposits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

Jean-Yves Reynaud and Robert W. Dalrymple


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14 Deep-Water Tidal Sedimentology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371

Mason Dykstra

15 Precambrian Tidal Facies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

Kenneth A. Eriksson and Edward Simpson

16 Hypertidal Facies from the Pennsylvanian Period:

Eastern and Western Interior Coal Basins, USA. . . . . . . . . . . . . . . . . . 421Allen W. Archer and Stephen F. Greb

17 Tidal Deposits of the Campanian Western

Interior Seaway, Wyoming, Utah and Colorado, USA . . . . . . . . . . . . . 437

Ronald J. Steel, Piret Plink-Bjorklund, and Jennifer Aschoff

18 Contrasting Styles of Siliciclastic Tidal Deposits

in a Developing Thrust-Sheet-Top Basins The Lower

Eocene of the Central Pyrenees (Spain). . . . . . . . . . . . . . . . . . . . . . . . . 473

A.W. Martinius

19 Holocene Carbonate Tidal Flats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507Eugene C. Rankey and Andrew Berkeley

20 Tidal Sands of the Bahamian Archipelago. . . . . . . . . . . . . . . . . . . . . . . 537

Eugene C. Rankey and Stacy Lynn Reeder

21 Ancient Carbonate Tidalites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567

Yaghoob Lasemi, Davood Jahani, Hadi Amin-Rasouli,

and Zakaria Lasemi

Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609


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Contributors

Hadi Amin-Rasouli Department of Geosciences, University of Kurdistan, Sanandaj,

Iran, [email protected]

Allen W. Archer Department of Geology, Kansas State University, Manhattan, KS

66506, USA, [email protected]

Jennifer Aschoff Department of Geology and Geologic Engineering, Colorado

School of Mines, Golden, CO, USA, [email protected]

Jesper Bartholdy Department of Geography and Geology, University of Copenhagen,

10 ster Voldgade, Copenhagen DK-3050, Denmark, [email protected]

Andrew Berkeley Department of Evironmental & Geographical Sciences,

Manchester Metropolitan University, John Dalton Extension Building, Chester

Street, Manchester M1 5GD, UK

Ilya Buynevich Department of Earth and Environmental Sciences, Temple

University, 313 Philadelphia, PA 19122, USA, [email protected]

Kyungsik S. Choi Faculty of Earth Systems and Environmental Sciences, Chonnam

National University, Gwangju 500-757, South Korea, [email protected]

Robert W. Dalrymple Department of Geological Sciences and Geological

Engineering, Queens University, Kingston, ON K7L 3N6, Canada, dalrymple@geol.

queensu.ca

Richard A. Davis, Jr. Department of Geology, Coastal Research Laboratory,

University of South Florida, Tampa, FL 33620, USA, [email protected]

Harte Research Institute for Gulf of Mexico Studies, Texas A&M University

Corpus Christi, TX 78412, USA

Mason Dykstra Department of Geology and Geological Engineering, Colorado

School of Mines, Golden, CO 80401, USA, [email protected]

Kenneth A. Eriksson Department of Geosciences, Virginia Tech, Blacksburg,

VA 24061, USA, [email protected]

Daidu Fan State Key Laboratory of Marine Geology, Tongji University, Shanghai

200092, China, [email protected]

Duncan FitzGerald Department of Earth Sciences, Boston University, Boston, MA


Burghard W. Flemming Senckenberg Institute, Suedstrand 40, 26382 Wilhelmshaven,

Germany, [email protected]


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xiv Contributors

Murray K. Gingras Department of Earth and Atmospheric Sciences, University of

Alberta, Edmonton, AB T6G 2E3, Canada, [email protected]

Steven L. Goodbred, Jr. Department of Earth and Environmental Sciences,

Vanderbilt University, Nashville, TN 37240, USA, [email protected]

Stephen F. Greb Kentucky Geological Survey, University of Kentucky, Lexington,

KY 40506, USA, [email protected]

Christopher Hein Department of Earth Sciences, Boston University, Boston, MA


Zoe J. Hughes Department of Earth Sciences, Boston University, Boston, MA 01778,

USA, [email protected]

Aitor A. Ichaso Department of Geological Sciences and Geological Engineering,

Queens University, Kingston, ON K7L 3N6, Canada, [email protected]

Davood Jahani Department of Geology, Faculty of Basic Sciences, North Tehran

Branch, Islamic Azad University, Tehran, Iran, [email protected]

Erik P. Kvale Devon Energy Corporation, 20 North Broadway, Oklahoma City, OK


Yaghoob Lasemi Illinois State Geological Survey, Prairie Research Institute,

University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA, ylasemi@

illinois.edu

Zakaria Lasemi Illinois State Geological Survey, Prairie Reserarch Institute,

University of Illinois at Urbana-Champaign, Champaign, IL 61820, USA,

[email protected]

James A. MacEachern Department of Earth Sciences, Simor Fraser Univeraity,

8888 University Drive, Burnaby, BC V5A 1S6, Canada, [email protected]

Duncan A. MacKay Department of Geological Sciences and Geological Engineering,

Queens University, Kingston, ON K7L 3N6, Canada, [email protected]

A.W. Martinius Statoil Research and Development, Arkitekt Ebbels vei 10, N-7005

Trondheim, Norway, [email protected]

Piret Plink-Bjorklund Department of Geology and Geologic Engineering, Colorado

School of Mines, Golden, CO, USA, [email protected]

Eugene C. Rankey Department of Geology, University of Kansas, 1475 Jayhawk

Blvd., 120 Lindley Hall, Lawrence, KS 66045, USA, [email protected]

Stacy Lynn Reeder Schlumberger-Doll Research, One Hampshire Street, Cambridge,

MA 02139, USA, [email protected]

Jean-Yves Reynaud Dpartement Histoire de la Terre UMR 7193 ISTeP, Musum

National dHistoire Naturelle, Gologie, CP 48, 43, rue Buffon, F-75005 Paris,

France, [email protected]

Yoshiki Saito Geological Survey of Japan, AIST, Central 7, Higashi 1-1-1, Tsukuba

305-8567, Japan, [email protected]


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xvContributors

Edward Simpson Department of Physical Sciences, Kutztown University, Kutztown,

PA 19530, USA,[email protected]

Ronald J. Steel Department of Geological Sciences, University of Texas Austin,

Austin, TX 78712, USA, [email protected]

Bernadette Tessier Morphodynamique Continentale et Ctire, University of Caen,

UMR CNRS 6143, 24 Rue des Tilleuls, 14000 Caen, France, [email protected]

Ping Wang Coastal Research Laboratory, Department of Geology, University of

South Florida, Tampa, FL 33620, USA, [email protected]


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2 E.P. Kvale

lamina is directly and positively related to tidal current

strength, which in turn is directly and positively related

to the magnitude of the daily rise and fall of the tide

(tidal range). Over periods of days, months, or years,

changes in tidal current strengths associated with

various lunar/solar cycles are mirrored by the change

in thicknesses of the vertically stacked laminae.Modern and ancient tidal rhythmites have been found

on every continent in the world except Antarctica. In

modern environments, tidal rhythmites occur in depos-

its associated with tide-dominated deltas, tidal embay-

ments, and estuaries. Tidal rhythmites can be used for

reconstructing ancient paleogeographies and paleocli-

mates (e.g. this chapter, Hovikoski et al. 2005; Kvale

et al. 1994), estimating paleotidal ranges (e.g. Archer

1995; Archer and Johnson 1997), understanding chan-

nel migration in the fluvio-estuaring transition (Choi

2010) determining lunar-retreat rates through time (e.g.

Williams 1989; Kvale et al. 1999), and most recently,

have been used to infer the major tidal constituents

associated with the tides that deposited them (e.g.

Kvale 2006). In order to understand tidal rhythmites,

however, one has to understand how tides are generated

and what controls their genesis.

The impact of diurnal, semidiurnal, and semimonthly

(neap-spring) tidal cycles on sediment deposition has

been well documented since the early 1980s (e.g. Visser

1980; Boersma and Terwindt 1981; Allen 1981). For

many geologists these became benchmark papers when

they were published because they showed how deposi-

tional packages within sedimentary successions can be

linked to a tidal origin. However, it was the discovery

of modern and ancient tidal rhythmites in the late 1980s

and 1990s that showed that a hierarchy of tidal cycles,

beyond simple semidaily, daily or fortnightly events,

could be preserved in the rock record (e.g. Kvale et al.

1989; Williams 1989; Dalrymple and Makino 1989;

Archer et al. 1991; Kvale et al. 1994; Miller and

Eriksson 1997). Tidal cycles associated with monthly,

semiannual, annual (usually includes a significant sea-

sonal climatic component), and even an approximately

18-year cycle have been identified from ancient tidal

rhythmites.

Studies, however, showed that the understanding of

one of the most basic of the tidal cycles, the neap-spring

or fortnightly tidal cycle, by most geologists, and

apparently many oceanographers, and astronomers as

well, was over-simplified. Many college-level textbooks

today continue to propagate a basic misunderstanding

of the neap-spring cycles and the origin of oceanic

tides in general (e.g. Duxbury et al. 2002).

The intent of this chapter is neither to outline a

history of the study of tides and tidal deposits nor to

document the current state of knowledge regarding

the history of the Earth-Moon system. These issues

are treated in some detail in Klein (1998), Rosenberg(1997), Williams (2000), and Coughenour et al.

(2009). Rather, it is to explain some basic tidal theory

and show how a more complete knowledge of ancient

tides can be extracted from the rock record. Most of

the information contained within this chapter is dis-

tilled from two summary papers: Kvale et al. (1999)

and Kvale (2006).

To truly understand tidal systems and, in particular,

the genesis of tidal rhythmites it is useful to understand

both an equilibrium tidal model and a dynamic tidal

model. The former explains the driving forces behind

the formation of tides and is commonly taught to

geology, oceanography, and astronomy undergraduates,

whereas the later, more accurately explains real-world

tides and is more useful in interpreting the rock record.

An understanding of both models is essential to anyone

who studies tides and tidal deposits, and both will be

discussed.

1.2 Equilibrium Tidal Theory

Most geologists understand tidal periodicities in the

context of equilibrium tidal theory. Tides are generated

by the gravitational forces of the Moon and, to a lesser

degree, the Sun on the Earth. The Moon accounts for

approximately 70% of the tide-raising force because of

its proximity to the Earth. In an equilibrium world, the

Earth is covered by an ocean of uniform depth that

responds instantaneously to changes in tractive forces

(MacMillan 1966). The equilibrium model can be used

to explain five of the six tidal periodicities that have

been commonly detected in rhythmite successions.

These six cycles are illustrated in Figs. 1.11.6(previ-

ously illustrated in Kvale et al. 1998). A seventh cycle

known as the nodal cycle, an approximately 18 year-

tidal cycle, and very well documented by Miller and

Eriksson (1997) within the Pride Shale, a lower

Carboniferous succession found in West Virginia, is

not illustrated here.

The figures each illustrate (from upper left to lower

right): A diagram and explanation of the equilibrium


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31 Tidal Constituents of Modern and Ancient Tidal Rhythmites: Criteria for Recognition and Analyses

tidal theory of five of the six tidal periods; a bar chart

of tidal height data (high tide elevations) from a modern,

real-world setting that shows how the astronomical

effects are reflected in cyclic changes in daily high

tides; a core from an ancient tidal rhythmite succession

showing how these cyclic tidal effects might be mani-

fested in a laminated tidal rhythmite; and a bar chart of

laminae thicknesses interpreted in the context of the

modern tidal cycle.

1.2.1 Semidiurnal (12.42 h)

Within the equilibrium tidal model, the interaction of

tidal forces from the Moon and Sun produce two oce-

anic bulges on opposite sides of the Earth (Fig. 1.1).

The rotation of a point on the Earth through these

bulges once a day produces two tides (the semidiur-

nal tide). Typically, these tides are not equal (termed

diurnal inequality), as one tide is higher (dominant)

than the other (subordinate) because the Moons

orbital plane and the Earths equatorial plane are not

parallel. The angular difference between the two

planes is termed lunar declination.

1.2.2 Synodic (29.53 Days)

Daily high tides are higher when the Earth, Moon, and

Sun are nearly aligned (full or new moon); this is

referred to as syzygy (Fig. 1.2). Conversely, lower

tides occur when the Sun and Moon are at right angles

to the Earth (first or third quarter phase), also known as

quadrature. Tides during full or new moon are

referred to as spring tides: spring in this context

refers to lively or energetic rather than implying a

seasonal connotation. Tides at quarter phases are

referred to as neap tides. The neap-spring tidal period

Fig. 1.1 Semidiurnal equilibrium model. (a) Two oceanic tidalbulges are produced on opposite sides of the Earth by the gravita-

tional forces of the Sun and the Moon. (b) Two tides are produced

each day by the spin of the Earth through these bulges. The diur-

nal inequality is produced when the tidal bulges are not centered

above the Earths equator. Semidiurnal tides can be recognized in

the rock record by the coupling of thick and thin lamina (c) and

graphically in the thickness measurements of laminated sequences

(d) as preserved in the tidal rhythmite succession from the

Pennsylvanian Mansfield Formation (Hindostan whetstone beds)

from Orange County, Indiana, USA (From Kvale and others

(1998) and used by permission from SEPM)


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4 E.P. Kvale

in the equilibrium model is related to the changing

phases of the Moon associated with the half-synodic

month. The synodic month (new moon to new moon,

or full moon to full moon) has a modern period of

29.53 days and encompasses two neap-spring cycles.

1.2.3 Tropical (Semidiurnal, 27.33 Days)

The tidal force also depends on the declination of the

Moon (Fig. 1.3). In this usage, declination refers to

the tilt or angle of the Moons orbit relative to the

Earths equatorial plane. The period of the variation in

declination is called the tropical month the interval of

time it takes the Moon to complete one full orbit from

its maximum northern declination to its maximum

southern declination and then return. The effect of the

tropical month in an equilibrium semidiurnal tidal

system is to cause the diurnal inequality of the tides.

Ideally, diurnal inequality is greatest when the Moon is

at its maximum declination. This inequality is reduced

to zero when the Moon is over the equator, producing a

crossover in the tidal data (Fig. 1.3). The current length

of the tropical month is 27.32 days (2 days shorter than

the synodic month see synodic discussion above).

Because of this difference, equatorial passages of the

Moon, called crossovers, have a shorter periodicity than

the periodicity related to synodic neap-spring tides.

1.2.4 Tropical (Diurnal, 27.32 Days)

In modern, dominantly diurnal systems (primarily

one tide per day), the tropical period described above

Fig. 1.2 Synodic equilibrium model. (a) In an equilibriumtidal model, spring tides occur when the Earth, Moon, and Sun

align during full or new moon (also known as syzygy).

Equlibrium neap tides occur when the Moon-Earth alignment is

90 from an Earth-Sun alignment (also known as quadrature).

The synodic month (currently 29.53 days) is the time it takes forthe Moon to orbit the Earth when measured from a new Moon

to the next new Moon. When neap-spring tides can be timed to

phases of the Moon they are referred to as synodic neap-spring

tides (Kvale 2006). (b) Graph of tidal heights of a portion of

the 1991 predicted high tides for Kwajalein Atoll, Pacific

(NOAA 1990) showing the effects of changing lunar phases.

(c) Portion of a core from the Mansfield Formation (Hindostan

whetstone beds), Indiana, USA with neap and spring tidal

deposits labeled. (d) Measurements of laminae thicknessesfrom Hindostan whetstone beds with neap and spring tidal

deposits labeled (From Kvale et al. (1998) and used by permis-

sion from SEPM)


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is responsible for generating neap-spring cycles. In

contrast to the synodic system, tides in a tropical sys-

tem behave as though the Suns gravitational effects

are dampened, which is impossible to explain in an

equilibrium tidal model (Fig. 1.4). In such cases, the

dominant tidal force depends on the declination of

the Moon relative to the Earths equator with the

force being greatest when the Moon is most directly

over the site in question. In these systems, the pre-

dicted and ancient tide data reveal that equatorial

passages of the Moon (crossovers) occur in phase

with the generation of neap-spring tides, in contrast

to the variable relationship exhibited by tropical

(semidiurnal) tides.

1.2.5 Anomalistic (27.55 Days)

Another tidal effect arises from the changing distance of

the Moon relative to the Earth during the lunar orbit

(Fig. 1.5). Because the lunar orbit forms an ellipse, with

the Earth slightly offset from the center, the Moon alter-

nates between perigee (closest approach to the Earth) and

apogee (the farthest distance from the Earth). During the

lunar synodic month there will be two spring tides (see

synodic periods described above). These spring tides,

however, will be of unequal magnitude producing alter-

nating high-spring and low-spring tides, which corre-

spond to spring tides during or near perigee (high spring)

and spring tides during or near apogee (low spring).

Fig. 1.3 Tropical, semidiurnal equilibrium model. (a) Model of theMoon in orbit around the Earth. The lunar declination is exaggerated

from its modern range of 1828. The tropical month (currently

27.32 days) is the time it takes for the Moon to move from its

maximum northern declination to its southernmost declination and

back to its northernmost declination in a single orbit. (b) Graph

of tidal heights of a portion of the same modern tidal record shown

in Fig. 1.2b illustrating diurnal inequality of semidiurnal tides.

Note diurnal inequality goes to zero when the Moon passes

directly over the Earths equator. (c) Image of core shown in

Fig. 1.2cshowing approximate position (labeled C) when Moon

was above the Earths equator during deposition. Note the approx-

imate equal thicknesses of the lamina on either side of the arrow.

(d)Bar chartshown in Fig. 1.2dwith arrows denoting passages

of the Moon above the Earths equator during deposition (From

Kvale et al. (1998) and used by permission from SEPM)


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6 E.P. Kvale

The semimonthly inequality of the spring tides disappears

when the Moon lies along the minor axis of the lunar

orbit and the difference in lunar distance is minimized

during subsequent spring tides. The time it takes for the

Moon to move from perigee to perigee is called the

anomalistic month, which is at present 27.55 days.

1.2.6 Semiannual (182.6 Days)

The synodic, tropical, and anomalistic periods have

slightly different values. Because of this, these periods

will interact constructively twice each year causing tidal

forces at these times to reach a maximum (as shown by

the dashed line in Fig. 1.6). In the equilibrium tidal

model, the date of this tidal maximum is a function of

latitude that is related to the declinational effects of the

Moon and Sun. An annual inequality has been docu-

mented in several ancient tidal rhythmite successions

(Kvale et al. 1994). This inequality is interpreted to be

climatic (non-tidal) in origin.

1.3 Dynamic Tidal Theory

As noted in the introduction, the equilibrium tidal

model explains the driving forces that cause tides but

does not explain real-world tides. For instance, the

Fig. 1.4 Tropical diurnal model. (a) Model of the Moon in itsorbit around the Earth (see Fig. 1.3a). (b) Graph showing the

1994 predicted relative high tides (mixed, predominantly diur-nal) for the Barito River estuary in Borneo (NOAA 1993). Note

the passages of the Moon above the Earths equator perfectly

track the neap tides and spring tides to the maximum declinations

of the Moon in its orbit around the Earth, a pattern not predicted

by equilibrium tidal theory. Such neap-spring tidal cycles are

termed tropical neap-spring tides (Kvale 2006). (c) Photograph

of a portion of a core from the Pennsylvanian Brazil Formation,

Daviess County, Indiana, USA. Arrowsindicate lamina depos-

ited with the Moon was above the Earths equator. (d)Bar chartof lamina thicknesses measured from core obtained from the

Brazil Formation. This unit also is mixed, predominantly diurnal.

Note the diurnal inequality of the semidiurnal component goes to

zero only in the neap tide deposits. This corresponds to the Moon

above the Earths equator during deposition (From Kvale and

others (1998) and used by permission from SEPM)


24/637


world does not spin through two tidal bulges. Instead,

oceanic tides rotate as waves around fixed (amphidro-

mic) points within individual ocean basins (Fig. 1.7).

Equilibrium tidal theory indicates that diurnal tides

should exist only at very high latitudinal positions,

which is not the case. For example, the Gulf of Mexico

and large tracts in the Indian and western Pacific oceans

are dominated by diurnal tides. Tides like those found

in Immingham, England, where the semidiurnal tides

have minimal diurnal inequality, cannot be explained

by equilibrium tidal theory, which requires such tides

to exist only in equatorial positions. Finally, equilib-

rium tidal theory does not explain neap-spring tidal

cycles which are synchronous with the 27.32 tropical

monthly period such as illustrated in Fig. 1.4.

The difficulties in understanding and explaining

real-world tides can be addressed by a dynamic tidal

model. This model is built around the concept of a

harmonic analysis of the components that compose

real-world tides. For instance, the Moon and Sun each

generate their own tide within the Earths oceans. Since

the orbits of the Earth around the Sun and the Moon

around the Earth are not perfectly circular, the ampli-

tude of the tides generated by each of these bodies, in

part, fluctuates depending on the Earths proximity

to the Sun and, much more importantly, the Moons

distance from the Earth. Periodically each of these

tides will constructively or destructively interact with

each other. The tides associated with changes in Moon-

Earth distance or Earth-Sun distance can be considered

to be a constituent of the overall tide, which can affect

any coastline.

To model these tidal constituents (also known as

tidal species) oceanographers conceptualize each

Fig. 1.5 Anomalistic equilibrium model. (a) Polar view of theMoon in orbit around the Earth. Note that lunar orbit is not

perfectly circular but somewhat elliptical (greatly exaggerated

in the diagram) and that the Earth is not position in the direct

center of the orbit path. The time it takes for the Moon to go

from perigee (closest approach) to apogee (furthest from the

Earth) and return is called the anomalistic month, which is27.55 days long at present. (b) Graph showing the 1992 pre-

dicted high tides for Saint John, New Brunswick, Canada

(NOAA 1991) showing the effects of the anomalistic month on

the Saint John tides. Note the semimonthly inequality goes to

zero when the Moon and Sun are aligned with the Moons

minor orbital axis (termed phase flip). (c) Photograph of a

core from the Mississippian Tar Springs Formation, Indiana,

USA showing the effects of the anomalistic month on neap-

spring tidal deposition. (d) Graph illustrating thicknesses as

measured between neap-to-neap tide deposits from the TarSprings Formation core, a portion of which is shown in

Fig. 1.5c. Note the position of the phase flip (From Kvale

et al. (1998) and used by permission from SEPM)


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8 E.P. Kvale

constituent as a phantom satellite that has its own

mass (that of the Moon, Sun, or a combination of the

two). Each phantom satellite has a motion within a

plane or is fixed relative to the stars and each generates

its own tide with a unique period, response time, and

amplitude (Pugh 1987) (Table 1.1). For instance S2

represents the twice-daily tide generated at a fixed

point on the Earth by a satellite that has the mass of

the Sun in a perfectly circular orbit around the Earths

equator. O1 represents the daily tide generated at a

fixed point on the Earth by a satellite with a mass of

the Moon and a motion above the Earths equator. For

each of the tidal constituents, the subscript indicates

if the tide is diurnal (1) or semidiurnal (

2).

The relative intensity for each of these tidal constitu-

ents along any oceanic coastline in the world can be

determined by a harmonic decoupling of an extended

hourly tidal record. These measurements typically are

recorded in most major harbors and other tidal stations

around the world. More than 100 tidal constituents have

been identified from a harmonic extraction of Earths

tides, however, seven of these (Table 1.1) account for

more than 80% of any real-world tide (Defant 1961).

The resonate amplification or destruction of these tidal

constituents determines the resulting tide for a specific

area within the Earths oceans (Fig. 1.8).

As noted above, each of these tidal constituents

corresponds to a unique tidal wave. These waves do

not travel around the world as predicted by equilibrium

tidal theory, but rather rotate around a point (referred

to as an amphidromic point) within a region of the

ocean at a speed determined by their constituents

orbital periodicity or the periodicity of the Earths spin

(Fig. 1.7). The location of these points is determined

by basin geometries and the Coriolis force.

Ideally, amphidromic circulation should be counter-

clockwise in the Northern Hemisphere and clockwise

in the Southern Hemisphere and never on the equator

Fig. 1.6 Semiannual equilibrium model. (a) View of the con-figuration of the Earth, Moon, and Sun representing the maxi-

mum spring tides formed when the Moon is at perigee, maximum

northern declination and new. Such spring tides occur every

182.6 days. (b) 1992 predicted high tides from Saint John, New

Brunswick, Canada (NOAA 1991) showing the effects of the

semiannual convergence of maximum spring tides. (c) Photograph

of a core from the Pennsylvanian Lead Creek Limestone, Indiana,

USA. In this core the neap-spring cycles thicken and thin in a

semiannual pattern. (d) Graph showing the thicknesses of

individual lamina from the Brazil Formation, Indiana. These

thicknesses are also organized into semiannual tidal cycles. Each

number records an individual neap-spring cycle (From Kvale

et al. (1998) and used by permission from SEPM)


26/637


but, as shown above, real-world tides dont always

follow convention and exceptions are known (Open

University Course Team 1999).

The major tidal cycles discussed under the equilib-

rium model can be understood in the context of the

dynamic model and tidal constituents. Specifically, the

synodic neap-spring cycle is generated through the

interaction of the S2and M

2constituents. In the modern

world, these two tides come into phase and amplify the

resulting tide every 14.77 days. The result is a syn-

odic spring tide. Conversely, every 13.66 days K1and

O1 converge and generate a tropical spring tide.Whether a spring tide along a specific coastline is

dominated by the synodic spring tide or the tropical

spring tide is determined by the basin geometry. For

instance, the Gulf of Mexico is dominated by the K1

and O1tides, therefore neap-spring tides cycle with the

tropical month (Fig. 1.9). The east coast of the USA,

however, is dominated by S2and M

2tides resulting in

neap-spring tides that cycle with the synodic month

(Fig. 1.9). The semimonthly inequality of spring tides

occurs because of the convergence of M2and N

2every

27.55 days. A diurnal inequality is driven by the inter-

action of O1and M

2(in phase once a day) and is noted

in coastal tides when these constituents are of suffi-

cient amplitude.

One can look at the progressive change in relative

intensity of particular tidal constituent along a coast

and see how that affects the resulting tides. For exam-

ple, Figs. 1.10and 1.11shows the amplitudes for the

seven dominant tidal constituents for the Gulf of

Carpentaria, Australia and the tidal patterns that result

from changes in the relative amplitudes of the various

constituents (from Kvale 2006). At the mouth of the

gulf at Booby Island, the tides are dominated by M2,

K1 and O

1. Given the dominance of O

1 and K

1, the

neap-spring cycle occurs every 27.32 days and corre-

sponds to the tropical monthly period. However, unlike

many regions whose neap-spring cycles are tropically

driven, there is a relatively strong M2tide (but relatively

weak S2 tide) at the mouth of the gulf. The resultant

Fig. 1.7 Diagram showing the amphidromic circulation for theM

2tide in the North Sea. Co-tidal lines indicate times of high

water. And co-range lines indicate lines of equal tidal range.

Figure is modified from Dalrymple (1992) which was based on

a map first drawn by J. Proudman and A. T. Doodson (From

information found in Cartwright 1999) (From Kvale (2006) and

used by permission from Marine Geology)

Table 1.1 List of the seven most common tidal constituents, their rotational speed (number of degrees a tidal wave generated bythe constituent can travel around its amphidromic point in 1 h), description, and period in solar hours (Defant 1961)

Tidal constituent Speed (degrees/hour) Origin Period in solar hours

M2

28.9841 Principal lunar 12.42

S2

30 Principal solar 12

N2

28.4397 Larger elliptical lunar 12.66

K2

30.0821 Combined declinational lunar

and declinational solar

11.97

K1

15.0411 Combined declinational lunar

and declinational solar

23.93

O1

13.943 Principal lunar 25.82

P1 14.9589 Principal solar 24.07


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10 E.P. Kvale

tide at Booby Island exhibits a tropically driven

neap-spring cyclicity comparable to the tide depicted

in Fig. 1.4except that it also exhibits a strong semidi-

urnal component that is driven by M2. Progressing fur-

ther south into the Gulf of Carpentaria, the strengths of

K1and O

1increase relative to M

2creating a tide that is

dominantly diurnal.

1.4 Ancient Tides

Some tidal rhythmites in the rock record preserve long

(several months worth), relatively complete succes-

sions of daily or semidaily tidal deposition. Particularly

complete records can be interpreted in the context of

the dynamic tidal model and several examples are

noted below.

1.4.1 Hindostan Whetstone Beds

(Pennsylvanian, Indiana)

Figures 1.2and 1.3show both a segment of core and a

bar chart of the laminae thicknesses from the Hindostan

Whetstone beds found in Orange County, Indiana

(Kvale et al. 1989). Neap-spring cycles in this chart

occur more frequently than crossovers indicating that

these tides were synodically driven and hence related

to the dominance of the M2and S

2over the O

1and K

1

constituents. Some caution is needed, however, in

interpreting crossover patterns because the absence of

a single half-day event could cause an apparent cross-

over. Ways to infer completeness of a tidal pattern are

discussed by Kvale et al. (1999). Suffice it to state that

with suitably long tidal rhythmite records, such as

presented here, it is possible to interpret crossover

patterns with some confidence.

This example clearly shows a diurnal inequality,

and, as such, O1must be significant. There appears to

be a lack of a pronounced semimonthly inequality

(anomalistic cycle) suggesting that N2 was relatively

weak. Therefore, tides that deposited the Hindostan

Whetstone beds were dominated by the constituents

M2, S

2, and O

1followed by K

1and N

2.

1.4.2 Brazil Formation (Pennsylvanian,Indiana)

Figure 1.4show a segment of core and a bar chart of

laminae thicknesses from the Brazil Formation of

Daviess County, Indiana (Kvale and Archer 1990;

Kvale and Mastalerz 1998). The neap-spring cycles in

this example occur at the same frequency as the cross-

overs indicating that these tides were driven by the

tropical period and hence reflect a dominance of O1

and K1 over S

2 and M

2. A weak semidiurnal signal

occurs during the neap tides and indicates that M2had

some amplitude and importance in the resulting tide.

The Brazil Formation rhythmites, like the whetstone

beds discussed above, lack a prominent semimonthly

inequality suggesting a weak N2 tidal constituent. It

can be inferred from this data base that the Brazil

Fig. 1.8 Resulting tide predicted from the stacking of 9 differenttidal constituents. Horizontal units are in hours (Modified from

MacMillan, 1966 in Kvale, (2006) and used by permission from

Marine Geology)


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Fig. 1.9 Graphs showing predicted high-data for two tidalreferences stations from the east coast and Gulf coast USA. The

Port Manatee example is typical of the tides in the Gulf coast

and the Hunniwell graph typifies east coast tides. Both tidal

records cover the same interval of time from January through

early May, 2005 (National Oceanographic and Atmospheric

Administration Web site 2004). Note that the equatorial pas-

sages of the Moon are fixed with the neap tides in the Gulf

coast station but move through the graph in the east coast exam-

ple. As such, Gulf coast neap-spring tides are driven by the

tropical month but the east coast neap-spring tides are controlled

by the phase changes of the Moon associated with the synodic

month (From Kvale (2006) and used by permission from Marine

Geology)


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12 E.P. Kvale

Fig. 1.10 Graphs andlocation map for predicted

high-tide data from three tidal

reference station in the Gulf

of Carpentaria, Australia.

The time interval for each

graph spans January through

early June, 2004 (AustralianNational Tidal Centre, Bureau

of Meteorology Web site,

2004) (From Kvale (2006)

and used by permission from

Marine Geology)


30/637


Formation tides were dominated by O1, K

1, followed

by M2with very weak contributions from S

2and N

2.

1.4.3 Abbott Sandstone (TradewaterFormation, Pennsylvanian, Illinois)

Figure 1.12shows an outcrop and bundle thicknesses from

some flaggy, large-scale tidal bundles along Interstate 57

in Johnson County, Illinois (Kvale and Archer 1991). A

histogram of bundle thicknesses indicates a strong semidi-

urnal signal throughout the record. While not as clean a

tidal record as the two previous examples, the Abbott

sandstone example appears to exhibit minimal diurnal

inequality during the neap tides. When the diurnal inequal-

ity tracks neap tides, it indicates that neap-spring cyclicity

is driven by the tropical period (e.g. Fig. 1.4). As such, the

Abbott Sandstone tidal record resembles that of Booby

Island, Australia (Fig. 1.10), in which M2, O

1and K

1dom-

inate the resultant tide over S2. There is a suggestion of a

semimonthly inequality to the Abbott sandstone record

indicating that N2was stronger than S

2 and sufficiently

strong to influence the tidal record.

These examples illustrate that tidal constituents

can be extracted from the rock record in well-preserved

tidal rhythmites. While it is not always possible to

draw conclusions regarding so many tidal constitu-

ents, deposits can generally be determined to be either

diurnal or semidiurnal in nature based on the absence

or occurrence of alternating thick-thin laminae. Most,

but not all, semidiurnal tidal deposits can be related

to the synodic period and the convergence of M2and

S2constituents. Exceptions of semidiurnal, tropically

driven neap-spring tides or tidal deposits, such as

Booby Island and the Abbott Sandstone, are known

and can be discerned if the tidal record is long and

clean enough. All diurnal deposits should have been

deposited in tropically driven neap-spring cycles.

Semidiurnal depositional systems that lack strong K1

or O1constituents (like Effingham, England), and in

which tidal sediments were deposited only on high

intertidal zones might mimic a diurnal tidal deposit

(Archer and Johnson 1997). In such a case, additional

outcrop work might result in the discovery of lower

intertidal or subtidal facies that would resolve the

issue.

Fig. 1.11 Line graph showing the changes in tidal amplitudefor the seven most dominant tidal constituents for several tidal

reference stations located along the eastern side of the Gulf of

Carpentaria (locations noted in Fig. 1.10. Constituent data was

extracted using the Seafarer Tides software package by the

Australian National Tidal Centre, Bureau of Meteorology and

provided to Kvale (2006) (From Kvale (2006) and used by per-

mission from Marine Geology)


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14 E.P. Kvale

1.5 Summary and Implications

The equilibrium tidal model is very useful for explain-

ing the gravitational forces that generate tides on the

Earth. However, it is an over-simplification and does not

explain the tides in most of the oceans of the world. To

explain real-world tides requires a basic understanding

of the dynamic tidal model. The dynamic tidal model

has been used to estimate changes in the Earth-Moon

distance through time (Williams 1989; Kvale et al.

1999) and has even been suggested as a way to better

understand the impact that tides have on biological

systems (Kvale 2006). It has also been used to model

tidal basin dynamics for determining the importance of

tidal facies within a basin or region (e.g. Ericksen and

Slingerland 1990; Wells et al. 2007). In the Abbott

example, an interpretation of neap-spring cyclicity could

be done with both the equilibrium and dynamic model,

but interpretation of the relative importance of the M2,

Fig. 1.12 Tradewater Formation, (a) Photo of the Abbottsandstone outcrop. This is part of a much more extensive

dune mesoform. Examples of dominant (D) and subordinate

(S) semidiurnal foresets are labeled. Rock hammer for

scale (lower part of photo) (b) Bar chart showing foreset

(depositional event) thickness variability with spring tides (S),

neap tides (N) and lunar crossover (arrows) events labeled.

Notice the semimonthly inequality of the spring tides related

to perigee and apogee effects. Also note that the lunar

passages of the equator (arrows) track the neap tide deposits

fairly closely suggesting that the neap-spring cycles are in

phase with the tropical month


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S2, O

1, K

1, and N

2constituents using the dynamic model

allows much more specific comparisons to be made to

real-world analogues (in this case Booby Island tides)

than would otherwise be possible. In fact, utilizing this

approach within the Illinois Basin one can interpret the

dominance of diurnal (O1and K

1) tides versus semidiurnal

(M2and S

2) tides for various tidal rhythmite packages

that span the Mississippian-Pennsylvanian systems

(Fig. 1.13). As Fig. 1.13shows, tidal rhythmites older

than the upper Morrowan Blue Creek Coal appear to

have been deposited within synodically driven systems

dominated by M2 and S

2. Younger tidal rhythmites

appear to have been deposited within tropically driven

systems. This change from synodically driven to tropically

driven tidal systems may reflect the closure of the

Iapetus Ocean during the early Pennsylvanian and a

Fig. 1.13 Stratigraphic chart for the Indiana portion of the IllinoisBasin showing stratigraphic intervals where good tidal rhythmite

records have been identified by the author. The solid grey line

marks the boundary below which tidal rhythmites seem to be con-

trolled primarily by the synodic monthly cycle and above which

the tidal rhythmites appear to reflect the tropical monthly cycle


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16 E.P. Kvale

major change in tidal dynamics within the midcontinent

Carboniferous sea of North America.

While teaching and understanding the dynamic

tidal system represents a bit of a paradigm shift to most

geologists, it creates possible research venues not

accessible through an understanding of equilibrium

tidal theory alone.

References

Allen JRL (1981) Lower Cretaceous tides revealed by cross-

bedding with mud drapes. Nature 289:579581

Archer AW (1995) Modeling of tidal rhythmites based on a

range of diurnal to semidiurnal tidal-station data. Mar Geol

123:110

Archer AW, Johnson TW (1997) Modeling of cyclic tidal

rhythmites (Carboniferous of Indiana and Kansas,

Precambrian of Utah, USA) as a basis for reconstruction ofintertidal positioning and paleotidal regimes. Sedimentology

44:9911010

Archer AW, Kvale EP, Johnson HR (1991) Analysis of modern

equatorial tidal periodicities as a test of information encoded

in ancient tidal rhythmites. In: Smith DG, Reinson GE,

Zaitlin BA, Rahmani RA (eds) Clastic tidal sedimentology.

Canadian Soc Petrol Geol Mem 16:189196

Boersma JR, Terwindt JHJ (1981) Neap-spring tide sequences

of intertidal shoal deposits in a mesotidal estuary.

Sedimentology 28:151170

Cartwright DE (1999) Tides: a scientific history. Cambridge

University Press, Cambridge, UK, 292 pp

Choi K (2010) Rhythmic climbing cross-lamination in inclined het-

erolithic stratification (IHS) of a macrotidal estuarine channel,Gomso Bay, west coast of Korea. J Sediment Res 80:550561

Coughenour CL, Archer AW, Lacovera KJ (2009) Tides,

tidalites, and secular changes in the Earth-Moon system.

Earth Sci Rev 97:5979

Dalrymple RW (1992) Tidal depositional systems. In: Walker

RG, James NP (eds) Facies models response to sea level

changes. Geological Association of Canada, St. Johns,

pp 195218

Dalrymple RW, Makino Y (1989) Description and genesis of

tidal bedding in the Cobequid Bay-Salmon River estuary,

Bay of Fundy, Canada. In: Taira A, Masuda F (eds)

Sedimentary facies in the active plate margin. Terra Science

Publication Co., Tokyo

Defant A (1961) Physical oceanography, vol 11. Pergamon, NewYork, 598 pp

Duxbury AB, Duxbury AC, Sverdrup KA (2002) Fundamentals

of oceanography, 4th edn. McGraw Hill, Boston, 344 pp

Ericksen MC, Slingerland R (1990) Numerical simulations

of tidal and wind-driven circulation in the Cretaceous

Interior Seaway of North America. Geol Soc Am Bull

102:14991516

Hovikoski J, Rsnen M, Gingras M, Roddaz M, Brusset S,

Hermosa W, Romero-Pittman L, Lertola K (2005) Miocene

semidiurnal tidal rhythmites in Madra de Dios, Peru. Geology

33:177180

Klein GD (1998) Clastic tidalites-a partial retrospective view.

In: Alexander C, Davis RA, Henry VJ (eds) Tidalites: pro-

cesses and products, vol 61, Special publication (SEPM

(Society for Sedimentary Geology)). Society of Sedimentary

Geology, Tulsa, pp 514

Kvale EP (2006) The origin of neap-spring tidal cycles. Mar

Geol 235:518

Kvale EP, Archer AW (1990) Tidal deposits associated withlow-sulfur coals, Brazil formation (lower Pennsylvanian),

Indiana. J Sediment Petrol 60:563574

Kvale EP, Archer AW (1991) Characteristics of two

Pennsylvanian-age semidiurnal tidal deposits in the Illinois

Basin, U.S.A. In: Smith DG Reinson GE Zaitlin BA Rahmani

RA (eds), Clastic tidal sedimentology. Canada Soc Petrol

Geol Mem 16:179188

Kvale EP, Mastalerz M (1998) Evidence of ancient freshwater

tidal deposits. In: Alexander C, Davis RA, Henry VJ (eds)

Tidalites: processes and products, vol 61, Special publication

(SEPM (Society for Sedimentary Geology)). Society of

Sedimentary Geology, Tulsa, pp 95107

Kvale EP, Archer AW, Johnson HR (1989) Daily, monthly, and

yearly tidal cycles within laminated siltstones of the Mansfieldformation (Pennsylvanian) of Indiana. Geology 17:365368

Kvale EP, Fraser GS, Archer AW, Zawistoski A, Kemp N, McGough

P (1994) Evidence of seasonal precipitation in Pennsylvanian

sediments in the Illinois Basin. Geology 22:331334

Kvale EP, Sowder KH, Hill BT (1998) Modern and ancient tides.

Poster and explanatory notes, SEPM, Tulsa, OK, and Indiana

Geological Survey, Bloomington, IN

Kvale EP, Johnson HW, Sonett CP, Archer AW, Zawistoski A

(1999) Calculating lunar retreat rates using tidal rhythmites.

J Sediment Res 69:11541168

MacMillan DH (1966) Tides. American Elsevier Publishing

Company, New York, 240 pp

Miller DJ, Eriksson KA (1997) Late Mississippian prodeltaic

rhythmites in the Appalachian Basin: a hierarchical record oftidal and climatic periodicities. J Sediment Res 67:653660

National Oceanographic and Atmospheric Administration

(2004) http://www.co-ops.nos.noaa.gov/tides04/ 2004 date

accessed, Sept

NOAA (1990) Tide tables 1991, high and low water predictions,

Central and Western Pacific Ocean and Indian Ocean, U.S.

Department of Commerce, National Oceanic and

Atmospheric Administration, Riverdale, Maryland

NOAA (1991) Tide tables, 1992 high and low water predictions,

Central and Western Pacific Ocean and Indian Ocean, U.S.



NOAA (1993) Tide tables, 1994 high and low water predictions,Central and Western Pacific Ocean and Indian Ocean, U.S.



Open University Course Team (1999) Waves, tides and shallow-

water processes, 2nd edn. Open University, Butterworth

Heinemann, Oxford, 227 p

Pugh DT (1987) Tides, surges and mean sea level. Wiley, New

York, 472 p

Rosenberg GD (1997) How long was the day of the dinosaur?

And why does it matter? In: Wolberg DL, Stump E,

Rosenberg GD (eds) Dinofest international: proceeding


34/637


symposium sponsored by Arizona State University, The

Academy of Sciences, Philadelphia, pp 493512

Visser MJ (1980) Neap-spring cycles reflected in Holocene sub-

tidal large-scale bedform deposits; a preliminary note.

Geology 8:543546

Wells MR, Allison PA, Piggott MD, Gorman GJ, Hampson GJ,

Pain CC, Fang F (2007) Numerical modeling of tides in the

late Pennsylvanian midcontinent seaway of North America

with implications for hydrography and sedimentation.

J Sediment Res 77:843865

Williams GE (1989) Late Precambrian tidal rhythmites in South

Australia and the history of the Earths rotation. J Geol Soc

Lond 146:97111

Williams GE (2000) Geological constraints on the Precambrian

history of Earths rotation and the Moons orbit. Rev Geophys

38:3759


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19R.A. Davis, Jr. and R.W. Dalrymple (eds.), Principles of Tidal Sedimentology,

DOI 10.1007/978-94-007-0123-6_2, Springer Science+Business Media B.V. 2012

2Principles of Sediment TransportApplicable in Tidal EnvironmentsPing Wang

Notations and Conventional Units

a: a reference level (typically defined at the top level

of the bedload layer) for suspended sediment con-

centration. (m)

c: suspended sediment concentration (dimension-

less for volume concentration, kg/m3for mass

concentration)

ca: reference concentration (dimensionless for vol-

ume concentration, kg/m3for mass concentration)

c(z): suspended sediment concentration profile

(dimensionless for volume concentration, kg/

m3for mass concentration)P. Wang (*)

Coastal Research Laboratory, Department of Geology,

University of South Florida, Tampa, FL 33620, USA

e-mail: [email protected]

Abstract

Physical processes of sediment transport in tidal environments are extremely

complicated and are influenced by numerous hydrodynamic and sedimentological

factors over a wide range of temporal and spatial scales. Both tide and wave forcingplay significant roles in the entrainment and transport of both cohesive and

non-cohesive particles. Present understanding of sediment transport is largely

empirical and based heavily on field and laboratory measurements. Sediment

transport is composed of three phases: (1) initiation of motion (erosion), (2) trans-

port, and (3) deposition. In tidal environments, the coarser non-cohesive sediments

are typically transported as bedload, forming various types of bedforms. The finer

cohesive sediments tend to be transported as suspended load, with their deposition

occurring mostly during slack tides under calm conditions. Rate of sediment

transport is generally proportional to flow velocity to the 3rd to 5th power. This

non-linear relationship leads to a net transport in the direction of the faster velocity

in tidal environments with a time-velocity asymmetry. Due to the slow settling

velocity of fine cohesive sediment and a difference between the critical shear stress

for erosion and deposition, scour and settling lags exist in many tidal environ-

ments resulting in a landward-fining trend of sediment grain size. The periodic

reversing of tidal flow directions results in characteristic bi-directional sedimen-

tary structures. The relatively tranquil slack tides allow the deposition of muddy

layers in between the sandy layers deposited during flood and ebb tides, forming

the commonly observed lenticular, wavy, and flaser bedding.


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20 P. Wang

c : depth averaged concentration (dimensionless

for volume concentration, kg/m3 for mass

concentration)

D: sediment grain size (m)

D*: dimensionless sediment grain size (dimension-

less)

Dw: wave-energy dissipation due to breaking(kg/s3)

dm: mean sediment grain size (m)

d50

: 50th percentile sediment grain size (m)

E: wave energy per unit water volume (kg/s2)

fc: bottom friction coefficient (dimensionless)

H: wave height (m)

h: water depth (m)

kd: empirical coefficients used in suspended sediment

concentration profile modeling (dimensionless)

kx: dispersion coefficient in x direction (dimen-

sionless)ky: dispersion coefficient in y direction (dimen-

sionless)

L: wave length (m)

Ls: turbulent mixing length (m)

Qb: volumetric bed-load transport rate (m3/m/s)

qs: volume rate of suspended sediment transport

(m3/m/s)

S = source and sink terms

s: sediment specific density =s/

w (dimension-

less)

T: wave period (s)

U: near bottom wave orbital velocity (m/s)

u(z): current velocity with respect to depthz(m/s)

u : depth-averaged current velocity (m/s)

u*: current related bed-shear velocity (m/s)

u*_c

: critical bed shear velocity (m/s)

u*_crs

: critical shear velocity for sediment suspension

(m/s)

cru : depth-averaged critical velocity (m/s)

v : depth average velocity inydirection (m/s)

ws: settling velocity (m/s)

ws_s

: settling velocity of single suspended particle

in clear water used in the calculation of the

settling velocity of flocs (m/s)

z: vertical coordinate representing water depth (m)

zo: vertical level with zero velocity, also often

referred to as bed roughness (m)

1: empirical coefficients used in suspended sedi-

ment concentration profile modeling (dimen-

sionless)

a2: empirical coefficients used in suspended sedi-


sionless)

b: empirical coefficients used in suspended sedi-


sionless)

s: sediment mixing coefficientq: Shields parameter (dimensionless)

qc: critical Shields parameter (dimensionless)

qcrs

: critical Shields parameter for sediment

suspension (dimensionless)

: Von Karmans constant, typically taken as 0.4

(dimensionless)

: an efficiency factor to incorporate the influ-

ence of bedforms on bedload transport used in

the Meyer-Peter and Mueller (1948) bedload

transport formula (dimensionless)

n: kinematic viscosity (m2/s)

s: sediment density (kg/m3)

rw: density of water (seawater in the case of tidal

environment) (kg/m3)

tb: bed shear stress (N/m2)

tc: critical bed shear stress (N/m2)

flocf : flocculation factor (dimensionless)

hs

f : hindered settling factor (dimensionless)

2.1 Introduction

Coastal sedimentology and morphodynamics are con-

trolled by a variety of interactive factors, including forces

from ocean tides and waves, trends and rates of sea-

level changes, sediment supply, climatic and oceano-

graphic settings, and antecedent geology. Depending

on the relative dominance of wave and tide forcing,

coastal environments can be classified as tide-dominated

and wave-dominated (Davis and Hayes 1984). This

chapter focuses on general physical processes of sedi-

ment transport that are applicable to the tide-dominated

environments. In this chapter, tidal environments are

defined generally as shallow marine environments that

are significantly influenced by tides.

The rise and fall of tides provide the main mecha-

nism for sediment transport and morphology changes

in tidal environments. In addition to generating tidal

current which constitutes the dominant forcing in tidal

environments, this regulated water-level fluctuation

can also modulate wave action. For example, higher


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212 Principles of Sediment Transport Applicable in Tidal Environments

waves were often measured at a fixed location on a

tidal flat during higher tides due to less friction related

wave dissipation (Lee et al. 2004; Talke and Stacey

2008). Sediment transport by wave forcing can be

significant locally, as well as during storm conditions.

Bottom shear stress, and therefore initiation of sedi-

ment motion and transport, is also strongly influencedby water depth, which varies substantially in tidal

environments. When the tidal water-level fluctuations

are confined by channels, e.g., tidal inlets and creeks,

strong tidal-driven flows can be generated. As com-

pared to other types of channelized flow, tidal flow

reverses direction periodically with a slack water period

in between, which may create unique bi-directional

sedimentary structures. In the case of tidal inlets

between barrier islands, large flood and ebb tidal deltas

can be deposited through the interaction of tide and

wave forcing. The cyclical rising, slacking, and fallingtide and the associated flow variation leave signature

sedimentary records through geological history, pro-

viding valuable information for understanding earth

history (e.g. Kvale et al. 1989).

Sediment grain size in tidal environment typically

ranges from non-cohesive medium sand to cohesive

clay. Compositionally, tidal sediments can be silici-

clastic, carbonate, and organic materials. A variety of

sedimentary structures, ranging from millimeter-scale

sand-mud laminations on tidal flats to subaqueous

dunes of tens of meters in tidal channels, exists in

tidal environments, indicating a wide range of sedi-

ment transport and deposition processes. Transport

and deposition of mixed cohesive and non-cohesive

sediments are poorly understood and provide cutting

edge research topics (Van Rijn 2007a, b, c)

Given the wide range of both cohesive and non-

cohesive sediments, and the energetic and highly vari-

able hydrodynamic processes driven by both tides and

waves, sediment transport processes in tidal environ-

ments are extremely complicated. This chapter aims

at providing a basic review of the principals of sedi-

ment transport applicable in tidal environments.

Various transport formulas and their general applica-

tions in tidal environments are discussed. It is worth

emphasizing that methods of computing the rates of

sediment transport are largely empirical, based

heavily on field and laboratory experiments.

Calibration and verification based on site-specific

data are essential to accurate applications of the formulas.

The transport principles and formulae can also be

applied qualitatively to interpret the sedimentary

processes observed in the field, and to design field

experiments. More detailed and further in-depth

mechanics of sediment transport can be found in

several dedicated texts, e.g., Mehta (1986b), Fredsoe

and Deigaard (1992), Nielsen (1992),Van Rijn (1993),

Pye (1994), Allen (1997), and Soulsby (1997).

2.2 Principles of Sediment Transport

Transport of sediment in coastal environments results

from the interaction between moving fluid (seawater in

this case) and sediment. Present knowledge on sedi-

ment transport processes is largely empirical, based on

numerous field and laboratory experiments. Insightful

parameterization is crucial in describing the compli-cated fluid-sediment interaction. In the following

section, key parameters describing fluid motion, sedi-

ment, and fluid-sediment interaction are discussed,

followed by the presentation of the commonly-used

methods for the calculation of non-cohesive and

cohesive sediment transport, respectively.

2.2.1 Fundamental Parameters

Fluid motion over a sediment bed exerts a horizontal

drag force and a vertical lift force. Generally, when

these forces overcome the gravity of a sediment grain,

transport is initiated. A theoretical analysis of the ini-

tiation of motion of an individual grain typically starts

with a force balancing between the drag-lift forces and

the gravitational force on the grain. The sediment grain

is put in motion if the moments of the fluid drag (FD

) and

lift (FL) forces exceed the moments of the submerged

gravitational force (FG) on the grain (Fig. 2.1). However,

due to our limited understanding of the very compli-

cated fluid-sediment interaction, sediment transport in

the natural environments cannot be quantified from the

force analysis of each grain. Instead, it is quantified

empirically through insightful parameterization of sediment-

fluid interaction, as discussed in the following.

When viscous fluid, e.g., seawater, flows over a sur-

face, a shear stress is generated by the fluid flow. This

shear stress is responsible for entraining and transport-

ing sediment. On the other hand, the friction at the

fluid-sediment interface exerts a drag on the fluid flow,


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22 P. Wang

yielding the commonly observed logarithmic velocityprofile over depth, i.e., the law of the wall:

*( ) ln

o

u zu z

zk

(2.1)

Where u(z) = current velocity with respect to depth,

z= vertical coordinate representing water depth,

u*= current related bed-shear velocity, = Von Karmans

constant, typically taken as 0.4, and zo= vertical level

with zero velocity, also often referred to as bed rough-

ness. A list of notation and conventional units are pro-

vided at the beginning of this chapter. Figure 2.2

illustrates an example of a logarithmic profile. The

dynamics of the bottom boundary layer where the cur-

rent velocity decreases rapidly with respect of depth is

crucial to sediment entrainment and transport. For plane

bed, the bed roughness (Fig. 2.2) is a function of sedi-

ment grain size. When bedforms exist, the bed roughness

is related to the geometry of the bedform. The bed shear

velocity is directly related to bed shear stress (tb) as:

2

*b wut r (2.2)

where rw= density of water (seawater in the case of tidal

environments). The bed shear velocity and bed shear

stress are two of the key parameters describing the fluid-

sediment interaction and are commonly used in comput-

ing sediment transport. Determining bed shear velocity

and bed shear stress can be difficult and often comprises

an essential part of a sediment transport study. By mea-

suring a velocity profile through the water column,

Eq. 2.1can be used to determine bed shear velocity and

bed shear stress, as well as the bottom roughness.

Another commonly used approach to determine the bot-

tom shear stress, especially for depth-averaged models,

is to relate bottom stress to velocity squared as:

21

2b w c

f ut r (2.3)

Fig. 2.1 Schematic forcebalancing of individual

grains on a horizontal bed

Fig. 2.2 An example of a logarithmic current profile, showing thebed roughness (z

o) and the schematic bottom boundary layer


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232 Principles of Sediment Transport Applicable in Tidal Environments

where fc is a bottom friction coefficient, determined

experimentally, and u = depth-averaged current velocity.

Equation 2.3describes the so-called quadratic friction

law, i.e., the friction exerted by a fluid flow is pro-

portional to its velocity squared. Equations 2.12.3

suggest that the faster the flow velocity and the rougher

the bed, the greater the shear stress, and therefore thegreater potential of sediment transport.

Although wave forcing is not the dominant factor in

determining the overall morphology and sedimentation

pattern in tidal environments, it is important in local

sediment entrainment and transport. For example,

numerous studies have shown that wave forcing can

have significant influence on the sedimentology and

morphodynamics of tidal flats (Christie et al. 1999;

Dyer 1998; Dyer et al. 2000; Li et al. 2000; Talke and

Stacey 2003, 2008; Lee et al. 2004). Wave motion can

be visualized as a circular motion of an imaginarywater particle. This wave orbital velocity, especially

near the bottom, can induce considerable shear stress

to entrain and transport sediment. Based on linear

wave theory, the maximum value of near bottom orbital

velocity (U) is:

2sinh

HU

hT

L

d

p

p

(2.4)

where h= water depth, L= wave length, T= wave

period, andH= wave height.

In a more simplified larger scale approach, wave-

induced sediment transport is often evaluated based on

the amount of energy that is carried by the wave.

Higher wave energy typically results in more active

sediment transport. Wave energy per unit water

volume (E) is determined as:

21

8 w

E gHr (2.5)

Equation 2.5shows that wave energy is proportional to

wave height squared, e.g., a 2 m wave will carry four

times the energy than a 1 m wave.

Waves break as they propagate from deep water

into shallow water. The energy that is carried by the

wave motion is dissipated rapidly through wave break-

ing. A large portion of this energy is expended to

transport sediment. Due to the intense turbulence gen-

erated by wave breaking, sediment transport associated

with wave breaking tends to be much greater than that

under non-breaking waves and a typical current.

Various empirical formulas were developed to evaluate

when waves break (Kaminsky and Kraus 1994),

one of the simplest and also reasonably accurate

formulas is:

0.78

b bH h (2.6)

where Hb= breaking wave height, h

b= water depth at

which waves break. In other words, waves break when

their height is about 80% of the water depth. Wells and

Kemp (1986) found that muddy bottoms, typical of

some tidal environments, can dissipate wave energy

to such an extent that the above breaking criterion is

never reached. Although wave forcing is secondary in

tidal environments, it can contribute significantly to

local sediment transport, especially in the ne

tidal sedimentology

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