9812819290

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edited by

Young C Kim

California State University, Los Angeles, USA

COASTAL AND

OCEAN ENGINEERING

N E W J E R S E Y • L O N D O N • S I N G A P O R E • B E I J I N G • S H A N G H A I • H O N G K O N G • TA I P E I • C H E N N A I

World Scientific

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British Library Cataloguing-in-Publication Data

A catalogue record for this book is available from the British Library.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN-13 978-981-281-929-1 ISBN-10 981-281-929-0

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Email: [email protected]

All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

Printed in Singapore.

HANDBOOK OF COASTAL AND OCEAN ENGINEERING

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Preface

Although coastal and ocean engineering is a very ancient field with the construction of Port A-ur near the mouth of the Nile in 3,000 BC, significant advances in this field have been made in the last several decades. The rise of interest in this field can be seen from the number of attendees by academics and practitioners in interna-tional conferences. The first Internainterna-tional Conference on Coastal Engineering was held in Long Beach, California in 1950 with less than 100 people. When the same conference was held in San Diego, California, in 2006, over 1000 delegates attended. In the last several decades, the world has seen significant coastal and ocean engi-neering projects, one of which is the Delta Project in the Netherlands. This project was designed to shorten and strengthen the total length of coast and dykes washed by the sea by closing off the sea arms in the Delta region. Other noteworthy coastal engineering projects include the Kansai Airport Project in Japan and, in recent years, the construction of mobile barriers at inlets to regulate tides in the Venice Lagoon known as the Venice Project. Interest in coastal and ocean engineering has arisen in recent years as humankind experiences coastal disasters that derive from coastal storm, hurricane and coastal flooding and seismic activities such as tsunamis, and the impacts of climate change which result in sea-level rise. The tsunami activity in Sumatra in December 2004 affected countries throughout the Indian Ocean and resulted in the loss of thousands of lives. Hurricane Katrina in New Orleans also claimed many lives with property damage exceeding $63 billion. Global warming and sea-level rise will affect shoreline retreats, inundate low coastal areas, damage coastal structures, and accelerate beach erosion. The need for better understanding of our coastal and ocean environment has risen considerably in recent years.

This handbook contains a comprehensive compilation of topics that are the forefronts of many technical advances in ocean waves, coastal and ocean engineering. It represents the most comprehensive reference available on coastal and ocean engineering to date, and it also provides the most up-to-date technical advances and latest research ﬁndings on coastal and ocean engineering. More than 70 internationally recognized authorities in the ﬁeld of coastal and ocean engineering contributed papers on their areas of expertise to this handbook. These interna-tional luminaries are from highly respected universities and renowned research and consulting organizations from all over the world.

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vi Preface

This handbook provides a comprehensive overview of shallow-water waves, water-level fluctuations, coastal and offshore structures, ports and harbors, coastal sediment processes, environmental problems, sustainable coastal development, coastal hazards, physical modeling, and coastal engineering practice and education. This book is an essential source of reference for professionals and researchers in the areas of coastal engineering, ocean engineering, oceanography, meteorology, and civil engineering, and as a text for graduate students in these fields. This handbook will be of immediate, practical use to coastal, ocean, civil, geotechnical, and struc-tural engineers, and coastal planners and managers as well as marine biologists and oceanographers. It will also be an excellent source book for educational and teaching purposes, and would be a good reference book for any technical library.

I would like to express my indebtedness to those who guided me and supported me as a mentor and a colleague throughout my professional life. They are:

Professor Robert L. Wiegel, University of California, Berkeley Professor Joe W. Johnson, University of California Berkeley Professor Robert G. Dean, University of Florida

Professor Fredric Raichlen, California Institute of Technology Professor Raymond C. Binder, University of Southern California Professor Shoshichiro Nagai, Osaka City University

Dr Basil Wilson, Science Engineering Associates Dr Lars Skjelbreia, Science Engineering Associates Dr Bernard LeMehaute, University of Miami

Professor Richard Silvester, University of Western Australia Mr Orville T. Magoon, Coastal Zone Foundation

Professor Billy L. Edge, Texas A&M University Professor Michael E. McCormick, US Naval Academy

Professor Yoshimi Goda, Yokohama National University and ECOH Corporation Professor Philip L.F. Liu, Cornell University

Professor Forrest M. Holly, The University of Iowa Dr Etienne Mansard, National Research Council, Canada Professor J. Richard Weggel, Drexel University

Mr Ronald M. Noble, Noble Consultants, Inc.

I also wish to express my indebtedness to those who nurtured me from my early teen years and changed my course of life. They are:

Dr Helen Miller Bailey, East Los Angeles College Mr H. Karl Bouvier, Jet Propulsion Laboratory

I extend my gratitude to my wife, Janet, for her constant support, encouragement, patience, and understanding while I was undertaking this task and to my daughter, Susan Calix, for proofreading some of the materials.

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Preface vii

Finally, I wish to express my deep appreciation to Ms Kimberley Chua of World Scientiﬁc Publishing Company who gave me invaluable support and encouragement from the inception of this handbook to its realization.

Young C. Kim

Los Angeles, California January 2008

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Contributors

Jonathan C. Allan Coastal Field Oﬃce

Oregon Department of Geology and Mineral Industries Newport, Oregon [email protected] William Allsop Technical Director HR Wallingford Wallingford, UK [email protected] Elena Sanchez Badorrey Associate Professor

CEAMA — Universidad de Granada Granada, Spain

[email protected]

Asuncion Baquerizo Associate Professor

Jurjen A. Battjes Emeritus Professor

Environmental Fluid Mechanics Section Delft University of Technology

Delft, The Netherlands [email protected] Michael J. Briggs

Research Hydraulic Engineer Coastal and Hydraulics Laboratory

U.S. Army Engineer Research and Development Center Vicksburg, Mississippi

[email protected]

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xiv Contributors

Tom Bruce

School of Engineering and Electronics University of Edinburgh

Edinburgh, UK [email protected] Subrata Chakrabarti

Joint Professor, Civil and Mechanical Engineering University of Illinois at Chicago

Chicago, Illinois [email protected] Peter J. Cowell Associate Professor School of Geosciences Institute of Marine Science University of Sydney Sydney, Australia Daniel T. Cox Professor

School of Civil and Construction Engineering Oregon State University

Corvallis, Oregon [email protected] Robert G. Dean

Graduate Research Professor of Coastal Engineering, Emeritus Department of Civil and Coastal Engineering

University of Florida Gainesville, Florida [email protected]ﬂ.edu Pierre Debaillon

Research Hydraulic Engineer

Centre d’Etudes Techniques Maritimes Et Fluviales (CETMEF) Compiegne, France

[email protected] Martijn P. C. de Jong

Formerly at Environmental Fluid Mechanics Section Delft University of Technology

Presently at Delft Hydraulics Delft, The Netherlands

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Contributors xv

Lesley Ewing

Senior Coastal Engineer California Coastal Commission San Francisco, California [email protected] Leopoldo Franco

Professor of Coastal Engineering Department of Civil Engineering University of Rome 3

Rome, Italy

[email protected] Panagiota Galiatsatou Research Associate

Department of Civil Engineering Aristotle University of Thessaloniki Thessaloniki, Greece

[email protected] Yoshimi Goda Professor Emeritus

Yokohama National University Adviser to ECHO Corporation Tokyo, Japan

[email protected] Ronald B. Guenther Professor Emeritus

Department of Mathematics Oregon State University Corvallis, Oregon [email protected] John Rong-Chung Hsu Professor

Department of Marine Environment and Engineering National Sun Yat-sen University

Kaohsiung, Taiwan Honorary Research Fellow

School of Civil and Resource Engineering University of Western Australia

Nedland, Australia [email protected]

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xvi Contributors

Robert T. Hudspeth

Professor and Director, Emeritus

Coastal and Ocean Engineering Program Oregon State University

Corvallis, Oregon

[email protected] Hwung-Hweng Hwung

Professor of Hydraulic and Ocean Engineering Director of Tainan Hydraulics Laboratory Department of Hydraulic and Ocean Engineering National Cheng Kung University

Tainan, Taiwan

[email protected] Masahiko Isobe

Professor and Special Adviser to the President Department of Sociocultural Environmental Studies Graduate School of Frontier Sciences

The University of Tokyo Chiba, Japan [email protected] Mamta Jain Coastal Engineer Halcrow Inc. Tampa, Florida [email protected] Bradley D. Johnson

Coastal and Hydraulics Laboratory

Shohachi Kakuno

Professor and Vice President Department of Civil Engineering Osaka City University

Osaka, Japan

[email protected] J. William Kamphuis

Professor of Civil Engineering, Emeritus Department of Civil Engineering Queen’s University

Kingston, Ontario, Canada [email protected]

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Contributors xvii

Akira Kimura Professor

Department of Social Systems Engineering Tottori University

Tottori, Japan

[email protected] Nobuhisa Kobayashi Professor and Director

Center for Applied Coastal Research University of Delaware

Newark, Delaware [email protected] Yukio Koibuchi Assistant Professor

Department of Sociocultural Environmental Studies Graduate School of Frontier Sciences

The University of Tokyo Chiba, Japan

[email protected] Paul D. Komar

Professor of Oceanography

College of Oceanic and Atmospheric Sciences Oregon State University

Corvallis, Oregon

[email protected] Andreas Kortenhaus

Leichtweiss-Institute for Hydraulics Technical University of Braunschweig Braunschweig, Germany

[email protected] Nicholas C. Kraus Senior Scientist

Coastal and Hydraulics Laboratory

[email protected] Alberto Lamberti

Professor

Department of Civil Engineering University of Bologna

Bologna, Italy

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xviii Contributors

Fang-Chun Lee

Kaohsiung, Taiwan Jiin-Jen Lee

Professor of Civil and Environmental Engineering Sonny Astani Department of Civil and

Environmental Engineering University of Southern California Los Angeles, California

[email protected] Yu-Cheng Li Professor

School of Civil Engineering Dalian University of Technology Dalian, China

[email protected] Miguel A. Losada Professor

Research Group on Environmental Flux Dynamics CEAMA — Universidad de Granada

Granada, Spain [email protected]

Etienne P. D. Mansard Executive Director

Canadian Hydraulics Centre National Research Council Canada Ottawa, Ontario, Canada

[email protected] Ashish J. Mehta

Professor of Coastal Engineering

Department of Civil and Coastal Engineering University of Florida

Gainesville, Florida [email protected]ﬂ.edu Michael D. Miles

Canadian Hydraulics Centre National Research Council Canada Ottawa, Ontario, Canada

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Contributors xix

Nobuhito Mori Associate Professor

Disaster Prevention Research Institute Kyoto University

Kyoto, Japan

[email protected] Tad S. Murty

Adjunct Professor

Department of Civil Engineering University of Ottawa

Ottawa, Ontario, Canada [email protected] Ioan Nistor

Assistant Professor

Ottawa, Ontario, Canada [email protected] Younes Nouri

Ottawa, Ontario, Canada Miquel Ortega

Associate Professor

[email protected] Hocine Oumeraci University Professor

Leichtweiss-Institute for Hydraulic Engineering and Water Resources

Technical University of Braunschweig Braunschweig, Germany

[email protected] Dan Palermo Assistant Professor

Ottawa, Ontario, Canada [email protected]

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xx Contributors

Andres Payo

Graduate School of Science and Technology University of Kumamoto

Kumamoto, Japan Krystian W. Pilarczyk

(Former) Manager, Research and Development Hydraulic Engineering Institute

Rykswaterstaat Delft, The Netherlands HYDROpil Consultancy Zoetermeer, The Netherlands [email protected] Panayotis Prinos

Professor of Hydraulic Engineering Department of Civil Engineering Aristotle University of Thessaloniki Thessaloniki, Greece [email protected] Tim Pullen Senior Engineer HR Wallingford Wallingford, UK [email protected] Alexander B. Rabinovich

P.P. Shirshov Institute of Oceanology Russian Academy of Sciences

Moscow, Russia

Department of Fisheries and Oceans Institute of Ocean Sciences

Sidney, B.C., Canada [email protected].

Roshanka Ranasinghe Associate Professor

UNESCO-IHE/Delft University of Technology Delft, The Netherlands

[email protected] Juan Recio

Leichweiss-Institute for Hydraulic Engineering and Water Resources

Technical University of Braunschweig Braunschweig, Germany

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Contributors xxi

Julie D. Rosati

Research Hydraulic Engineer Coastal and Hydraulics Laboratory U.S. Army Corps of Engineers Mobile, Alabama

[email protected] Peter Ruggiero

Assistant Professor

Department of Geosciences Oregon State University Corvallis, Oregon

[email protected] Murat Saatcioglu

Professor

Ottawa, Ontario, Canada [email protected] Juan M. Santiago

Associate Professor

[email protected]

Holger Schuttrumpf Professor and Director

Institute of Hydraulic Engineering and Water Resources Management RWTH — Aachen University Aaachen, Germany

[email protected] Richard Silvester

Professor Emeritus

School of Civil and Resource Engineering University of Western Australia

Nedland, Australia [email protected]

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xxii Contributors

Marcel J. F. Stive Professor and Director Delft Water Research Centre

Department of Hydraulic Engineering Delft University of Technology Delft, The Netherlands [email protected] Kyung-Duck Suh Professor

Department of Civil and Environmental Engineering Seoul National University

Seoul, Korea [email protected] Shigeo Takahashi

Executive Researcher and Director Tsunami Research Center

Port and Airport Research Institute Yokosuka, Japan

takahashi [email protected] Klemens Uliczka

Research Hydraulic Engineer

Federal Waterways Engineering and Research Institute (BAW) Hamburg, Germany

[email protected] Jentsje van der Meer Principal

Van der Meer Consulting Heerenveen, The Netherlands [email protected] Marc Vantorre

Professor

Division of Maritime Technology Ghent University

Ghent, Belgium

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Contributors xxiii

Todd L. Walton Director

Beaches and Shore Resource Center Florida State University

Tallahassee, Florida [email protected] Xiuying Xing

Graduate Research Assistant

Sonny Astani Department of Civil and Environmental Engineering University of Southern California

Los Angeles, California Harry Yeh

Professor

School of Civil and Construction Engineering Oregon State University

Corvallis, Oregon [email protected] Dong Hoon Yoo Professor

Department of Civil Engineering Ajou University

Suwon, Korea [email protected] Sung Bum Yoon Professor

Department of Civil and Environmental Engineering Hanyang University

Ansan, Korea

[email protected] Melissa Meng-Jiuan Yu

Kaohsiung, Taiwan Barbara Zanuttigh Assistant Professor

Department of Civil Engineering University of Bologna

Bologna, Italy

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The Editor

Young C. Kim, PhD, is currently a Professor of Civil Engineering, Emeritus at California State University, Los Angeles. Other academic positions held by him include a Visiting Scholar of Coastal Engineering at the University of Cali-fornia, Berkeley (1971); a NATO Senior Fellow in Science at the Delft University of Technology in the Netherlands (1975); and a Visiting Scientist at the Osaka City University for the National Science Foundations’ US–Japan Cooperative Science Program (1976). For more than a decade, he served as Chair of the Department of Civil Engineering and recently he was Associate Dean of the College of Engineering. For his dedicated teaching and outstanding professional activities, he was awarded the university-wide Outstanding Professor Award in 1994.

Dr Kim was a consultant to the US Naval Civil Engineering Laboratory in Port Hueneme and became a resident consultant to the Science Engineering Associates where he investigated wave forces on the Howard-Doris platform structure, now being placed in Ninian Field, North Sea.

Dr Kim is the past Chair of the Executive Committee of the Waterway, Port, Coastal and Ocean Division of the American Society of Civil Engineering (ASCE). Recently, he served as Chair of the Nominating Committee of the International Association of Hydraulic Engineering and Research (IAHR). Since 1998, he served on the International Board of Directors of the Paciﬁc Congress on Marine Science and Technology (PACON). He currently serves as the President of PACON. Dr Kim has been involved in organizing 10 national and international conferences, has authored three books, and has published 52 technical papers in various engineering journals.

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Chapter 1 Wave Setup

Robert G. Dean

Department of Civil and Coastal Engineering University of Florida, Gainesville, FL, USA

[email protected]

Todd L. Walton

Beaches and Shores Resource Center Florida State University, Tallahassee, FL, USA

[email protected]

Wave setup is the increase of water level within the surf zone due to the transfer of wave-related momentum to the water column during wave-breaking. Wave setup has been investigated theoretically and under laboratory and field conditions, and it includes both static and dynamic components. Engineering applications include a significant flooding component due to severe storms and oscillating water levels that can increase hazards to recreational beach goers and can contribute to undesirable oscillations of both constructed and natural systems including harbors and moored ships. This chapter provides a review of the knowledge regarding wave setup and presents preliminary recommendations for design. It will be shown that wave setup is not adequately understood quantitatively for engineering design purposes.

1.1. Introduction

Wave setup was brought to the attention of coastal engineers and scientists in the 1960s (i.e., see Ref. 1, p. 245) after the initial theoretic developments of Longuet-Higgins2 and Longuet-Higgins and Stewart3,4 along with limited ﬁeld observations and laboratory studies supported the existence of wave setup, the magnitude of which was observed to be in the order of 10–20% of the incident wave height. It was noted in early ﬁeld observations that water levels on the beach were higher than those recorded by a tide gauge at the end of a pier suggesting a wave setup physically forced by wind waves and swell.

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2 R. G. Dean and T. L. Walton

Fig. 1.1. Deﬁnition sketch. Energy and momentum are transferred from winds to waves in the generating area. The waves convey energy and momentum to the surf zone where the waves break. Upon breaking, the energy is dissipated and the momentum is transferred to the water column resulting in longshore and onshore forces exerted on the water column.

Wave setup is the additional water level that is due to the transfer of wave-related momentum to the water column during the wave-breaking process. As waves approach the shoreline, they convey both energy and momentum in the wave direction. Upon breaking, the wave energy is dissipated, as is evident from the turbulence generated; however, momentum is never dissipated but rather is trans-ferred to the water column resulting in a slope of the water surface to balance the onshore component of the ﬂux of momentum (see Fig. 1.1). If waves are irregular, in addition to a steady wave setup, the setup includes a dynamic component that oscillates with the wave group period and there may be a weak resonance within the nearshore amplifying this oscillating component. These have been termed infra-gravity waves and are more dominant for narrow banded spectra both in frequency and in directional spreading. The oscillatory component is denoted “dynamic wave setup” in this chapter.

This chapter discusses the significance of wave setup to coastal engineering design, provides a review of the classical linear wave theory of wave setup, reviews results from laboratory and field studies, summarizes results and recommends pre-liminary design approaches for the static component. To provide a “look ahead,” we will see that the phenomenon of wave setup is not yet adequately understood for satisfactory engineering calculations and that the effects of profile slope are very

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Wave Setup 3

signiﬁcant. The interested reader is also referred to an earlier review article on wave setup by Holman.5

1.2. Engineering Significance of Wave Setup

Wave setup (both static and dynamic components) is relevant to a number of engi-neering applications. The contributions of wave setup under extreme storm events can be substantial, adding several feet to the elevated water levels. The interaction of wave setup with vegetation differs from wind surge and thus it is important to differentiate the two components, for example in ascertaining the benefits of wet-lands in reducing wave setup. Finally, the oscillating component of wave setup is relevant to beach safety in some locations and to many natural and constructed coastal systems that have the capability to resonate including harbors and moored ships.

1.3. Terminology and Related Considerations

Standard terminology defines the water level in the absence of wave effects as “still water level,” whereas wave setup will cause a departure from the still water level and this water level including the effects of the waves is the “mean water level.” As implied, the mean water level is determined as the average of the fluctuating water level over a suitable time frame usually taken as a number of multiples of the short wave period, say the spectral peak. In considering wave setup, often the location of interest is that of the maximum wave setup at the shoreline. This raises the question of whether wave setup is defined at elevations above the maximum rundown, say on the beach face where the water is present over only a portion of the wave period. Since wave setup is defined as the mean water level, over what period should the water surface be averaged on the beach face which is “wetted” over only a portion of the wave period? If the time average is over only the portion of the period that water is present, in the upper limit, the maximum setup will be the maximum runup. For purposes here, wave setup will usually be defined only for conditions where water is present over a full wave period.

When calculating wave runup on a structure such as a levee or revetment, the question arises whether it is appropriate to ﬁrst calculate wave setup and then add the wave runup which is usually empirically based on model results. In the more recent empirical results (e.g., the TAW method, see Ref. 6), the runup is expressed as a proportion of the signiﬁcant wave height at the base of the steeper slope (e.g., at a revetment or levee). The wave runup determined in the model on which the method was based generally included some wave setup (or setdown) seaward of the toe of the slope and included wave setup landward of the toe of the slope. Thus, in the application of interest, the most appropriate approach is to calculate and include wave setup at the toe of the slope; however, recognizing that the measured landward runup includes setup, no additional setup should be added explicitly landward of the toe of the slope.

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1.4. A Brief Review of Wave Setup Mechanics

1.4.1. Static wave setup for monochromatic waves

Longuet-Higgins2_{and Longuet-Higgins and Stewart}3,4_{were the first to formalize the} notion of wave momentum flux and its relationship to wave setup. The momentum flux, S_ij, is a second-order tensor given by

S_xx= E n(cos2_{θ + 1) −}1 2 , S_yy= E n(sin2_{θ + 1) −}1 2 , S_xy= S_yx= E 2 sin 2θ, (1.1)

where E is the wave energy density, n is the ratio of wave group velocity to wave celerity and θ is the angle between the wave direction and the x-axis. The term

S_xy reads “the ﬂux per unit width, in the x-direction, of the y-component of momentum,” etc.

The steady-state equations of motion obtained by time averaging over the short wave period are, including the eﬀects of wind stress and bottom friction:

∂ (ηwind+ ηwave) ∂x =− 1 ρg(h + η) _∂S xx ∂x + ∂S_xy ∂y −τsx+ τbx and ∂ (η_wind+ η_wave) ∂y =− 1 ρg(h + η) _∂S yy ∂y + ∂S_yx ∂x −τsy+ τby . (1.2)

In the above,ηwindis the surge component due to the wind stress, ηwaveis the wave setup, ρ is the mass density of water, g is the gravitational constant, h is the local water depth, τ_sx and τ_bx are the surface and bottom shear stresses, respectively, and similarly for the y-direction. The coordinate direction, x is oriented shoreward and a right-handed coordinate system is considered.

The most simple solution is for waves propagating directly shoreward (S_xy= 0) in which the surface and bottom stresses are considered negligible, and all variables are considered uniform in the y-direction. The resulting equation is

∂η_wave ∂x =− 1 ρg(h + η) _∂S xx ∂x . (1.3)

To proceed, we need to determine a boundary condition forη_wave,a _{at the seaward} end of the surf zone. Longuet-Higgins7 _{has shown that in the absence of energy} dissipation, the following general relationship for η applies

η = C − 1

2g(u 2− w2₎

η=0, (1.4)

a_{For purposes of convenience, hereafter the subscript on}_η

wavewill be omitted such that the wave setup is simply denoted asη.

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Wave Setup 5

where u2 _{and w}2 _{represent the time averages of the square of the ﬁrst-order} hori-zontal and vertical wave velocities evaluated at the mean water surface, respectively. Equation (1.4) is a type of a Bernoulli equation for unsteady ﬂows which, when eval-uated at the break point and considering no wave setup in deep water to evaluate the constant, C = 0, the setup is negative (setdown) and given by

η_b=− H

2

bkb

8 sinh 2k_bh_b, (1.5)

where H_b is the breaking wave height and k_b is the wave number at breaking. For shallow water conditions and depth limited breaking (H_b = κ(h_b+ η_b)), Eq. (1.5) yields

η_b =−κHb

16 . (1.6)

As an example, for a κ value of 0.78, the wave setdown is approximately 5% of the breaking wave height.

With the seaward boundary condition now established, for the case of shallow water wave-breaking and the consideration of depth limited breaking across the surf zone, the wave setup is

η = −κHb

16 +

3κ2_/8

(1 + (3κ2/8))(hb− h) . (1.7)

It is noted that in the above equation, the bottom shear stress has been taken as zero and that a shoreward directed bottom shear stress on the water column as would occur due to undertow would increase the wave setup. As examples, the ratio of wave setup to breaking height at the still water line (h = 0) and at the location of maximum wave setup (η =− h) for a κ value of 0.78 are

F0|κ=0.78 ≡ η(h = 0, κ = 0.78) H_b = 5κ 16(1 + (3κ2/8)) κ=0.78 = 0.198 (1.8) and Fmax|_κ=0.78 ≡η(h = − η, κ = 0.78) H_b = F0 1 + 3κ 2 8 κ=0.78 = 5κ 16 κ=0.78 = 0.244 . (1.9) It is seen that the wave setup is strongly dependent on the value of the breaking ratio

κ which will be shown to decrease with decreasing beach slope. Figure 1.2 presents

the ratios, F0and Fmaxversus κ. It is useful to relate κ in an approximate manner to beach slope. Although there is not a one-to-one correspondence, Fig. 1.3 is based on the Dally et al.8wave-breaking model and provides an approximate correspondence between uniform proﬁle slope and the associated κ value. It is evident that the Dally et al. model provides reasonable κ values for smaller beach slopes (say less than about 0.06), but the κ values are too large for steeper slopes.

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6 R. G. Dean and T. L. Walton 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 Kappa Fo Fmax Fo a n d Fm a x

Fig. 1.2. Values ofF0 andFmax versus wave-breaking index,κ (kappa).

0.00 0.02 0.04 0.06 0.08 0.10 Profile Slope 0.0 0.5 1.0 1.5 2.0 Kap pa

Fig. 1.3. Relationship between proﬁle slope andκ (kappa) value. Based on Dally et al.8 wave-breaking model.

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Wave Setup 7

1.4.2. Eﬀects of wave nonlinearity

Wave nonlinearity depends on the following parameters: H/L0 and h/L0. The nonlinearity is exhibited in the wave profile by peaked crests and flatter troughs and increases with wave height and shallow water. Somewhat surprisingly, the momentum fluxes in shallow water are less for nonlinear waves than for linear waves of the same height. This is primarily because the momentum fluxes are proportional to wave energy (Eq. (1.1)) and the wave energy is proportional to the root-mean square of the water surface displacement that is less for nonlinear waves with long troughs and peaked wave crests. Figure 1.4 presents the ratio of nonlinear to linear momentum fluxes as determined by Stream Function wave theory.9–11 _{The reason} that the quantities for nonlinear waves are greater in deep water than for linear waves is that the nonlinear calculations extend up to the actual free surface whereas the linear quantities only extend up to the mean free surface.

1.4.3. Role of wave directionality

Equation (1.1) demonstrates that for a given wave height, the maximum shoreward ﬂux of onshore momentum occurs for normally incident waves (θ = 0◦). Thus as expected for directional waves, the S_xx term is reduced. However, this reduction is relatively small as can be demonstrated by considering a breaking wave direction of 30◦relative to a beach normal (this represents a reasonably large wave obliquity

10-3.000 2 3 4 5 6₁₀-2.000 2 3 4 5 6 ₁₀-1.000 2 3 4 5 5 ₁₀0.000 2 3 4 5 6 ₁₀1.000 h/L_o 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Ratio o f Non lin ear to Lin ear Mo m e nt um Flu x H/H b =0.2 5 H/H b=0 .75 H/H b =1.0 H/H b=0 .50

Fig. 1.4. Ratio of nonlinear to linear wave momentum ﬂux,Sxx, for forty stream function wave combinations.12

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at breaking). The reduction in S_xxfor a wave of given height and for shallow water conditions is 16.7%.

1.4.4. Eﬀects of vegetation

The effects of vegetation have been shown to result in a reduced setup and, in some cases, may cause a setdown.12For linear waves, vegetation protruding through the water surface experiences a net drag force (quadratically related to velocity) on the vegetation in the direction of wave propagation and, of course, there must be an equal and opposing force exerted on the water column. This opposing force acting on the water column partially counteracts the force due to momentum transfer and thus reduces the wave setup (similar to an offshore directed wind stress). For linear waves and vegetation which is submerged during the entire wave passage, no net vegetation-related force exists on the water column and thus there is no effect on the wave setup. However, due to the character of nonlinear waves with higher and shorter shoreward velocities under the wave crests, even if the vegetation is fully submerged during the passage of the wave, a net drag force is induced on the vegetation in the wave propagation direction again resulting in a reduction in the wave setup and, for some cases, a wave setdown.

1.4.5. Dynamic wave setup

It is noted that theoretical formulations of the dynamic wave setup must include the time dependent terms in the counterparts of Eq. (1.2). The dynamic wave setup or “surf beat” was first identified through field observations and measurements by Munk13 _{and Tucker.}14 _{A number of theoretical treatments of dynamic wave setup} based on various hypotheses have been developed with each focusing on a different mechanism. These include Symonds et al.15 _{(time-varying breakpoint), Symonds} and Bowen16_{(trapping of long waves by longshore bars), Schaffer and Svendsen}17 (reinforcement of incoming and reflected long waves), etc. Kostense18 _conducted laboratory experiments to investigate the dynamic setup component and found that the results were in qualitative agreement with the theory of Symonds et al.15

We can apply the results for monochromatic waves to investigate the approx-imate dynamic wave setup for a simple irregular wave case. Consider a bichromatic wave system with wave heights H1 and H2 (H1 > H2) and a small frequency dif-ference between the two components. If the resulting wave group varies so slowly that static conditions occur within the surf zone, Eq. (1.7) applies and is written as

η = F H_b, (1.10)

where H_b is the breaking wave height and F is a proportionality factor depending on whether the referenced setup is at the still water shoreline or the maximum wave setup (see Eqs. (1.8) and (1.9)). The maximum and minimum wave setup values are:

ηmax= F (H1+ H2) ,

ηmin= F (H1− H2) .

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Wave Setup 9

Table 1.1. Static and dynamic wave setup characteristics for a biharmonic wave system.

H2/H1 ηmax/F H1 ηavg/F H1 (ηmax− ηavg)/ηavg

0.2 1.2 1.01 0.19

0.4 1.4 1.04 0.35

0.6 1.6 1.09 0.47

0.8 1.8 1.16 0.55

1.0 2.0 1.27 0.57

It can be shown that the average wave setup depends on the ratio H2/H1as shown in Table 1.1. The fourth column presents the ratios of the maximum dynamic wave set amplitude to the average wave setup component.

In the case with H2= H1, the dynamic wave setup displacement from the mean setup equals 57% of the average wave setup (Table 1.1, Column 4).

In the above, we have examined the dynamic wave setup for the case of a simple bichromatic wave system in which the diﬀerence in frequencies of the two com-ponents was fairly small. For the case of a wave spectrum, the situation is much more complex with, for the case of a narrow spectrum, the group envelope varying according to the Rayleigh distribution. For the case of a wide spectrum, the dynamic component is reduced considerably.

1.5. Laboratory and Field Measurements of Wave Setup

Having reviewed the theory of wave setup and its relationship to various factors, the two sources available for evaluation are laboratory and ﬁeld data.

1.5.1. Laboratory experiments on wave setup

Many laboratory investigations of static and dynamic wave setup have been con-ducted. The results of an early laboratory investigation with monochromatic waves by Bowen et al.19_{are shown in Fig. 1.5. For this study, the ratio of maximum wave} setdown and wave setup on the beach face to breaking wave height are− 0.035 and + 0.316, respectively, compared with − 0.049 and + 0.244 on the beach face for a

κ value of 0.78. The eﬀect of beach slope has been noted earlier and the relatively

large beach slope of 0.082 in these experiments is undoubtedly a contributor to the large setup value. Later, laboratory investigations have included examination of irregular waves including measurements of water particle velocities and pressures which form the basis of the S_xxmomentum ﬂux component.

Battjes20 conducted one of the earliest laboratory studies of wave setup due to irregular waves. Setup was measured through bottom mounted manometers and it was found that the wave setup was less than predicted. It was hypothesized that this diﬀerence was possibly due to air in the water column of the manometers. The entire setup was shifted landward relative to the theoretical and this delay was later attributed to a “roller” that is transported along with the wave crest region and

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Fig. 1.5. Measured wave setup and setdown in the laboratory.19

conveys wave energy and momentum landward prior to transfer of the momentum to the water column and the associated wave setup.21_{Later, Stive and Wind}22 con-ducted a very detailed laboratory investigation in which they demonstrated the role of wave nonlinearity. In this study, the momentum ﬂux components (velocities and pressures) were measured to the degree possible and it was found that the calcu-lated wave setup based on nonlinear wave theories was in much better agreement with measured wave setup than calculations based on linear wave theories. In these comparisons, it was not necessary to introduce the roller concept.

The two laboratory studies reviewed above have focused on static setup and it has been noted that irregular waves also produce dynamic wave setup. Hedges and Mase23 _{have presented an interesting reanalysis of earlier runup laboratory} measurements by Mase24_{in which irregular waves provided the forcing.}b_{The planar} slopes represented in the data were: 1:5, 1:10, 1:20, and 1:30. Figure 1.6 presents an example of the form in which the data were plotted where the horizontal axis is

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Wave Setup 11

Fig. 1.6. Variation of nondimensional runup with Iribarren number.23

the Iribarren number, ξ0 deﬁned as

ξ0=

tan α

H/L (1.12)

in which tan α is the proﬁle slope. The interpretation of Fig. 1.6 is that for a zero slope (zero Iribarren number), there would be no short wave runup; therefore, the intercept represents the sum of the static and dynamic components of wave runup. Equations of the following form were ﬁt to plots of the type of Fig. 1.6:

Rchar

H1_/3

=Schar

H1_/3

+ ccharξ0, (1.13)

where the subscript “char” refers to the percent associated with the variable; for example, the 2% runup is defined as R2%. It was found that both Scharand ccharwere Rayleigh distributed with S1/3 and c1/3 equal to 0.27 and 1.04, respectively, where only the first term represents wave setup and is of interest here. The results for Schar can be interpreted in terms of the static and dynamic wave setup components. As an example, Smean= 0.17 and S2%= 0.37. Thus, the 2% value of the nondimensional dynamic setup defined here as ∆S2% is

∆S2%=

ηdyn,2%

H1/3

= (S2%− Smean) = (0.37− 0.17) = 0.20 . (1.14) Thus, the mean setup at the still waterline is 17% of the signiﬁcant wave height measured at the toe of the slope and the 2% dynamic component at the still waterline is 20% of the signiﬁcant wave height at the toe of the slope or slightly larger than the mean wave setup. These results are interesting and of reasonable magnitudes; however, there are two problems with recommending them for universal application. First, we know that the mean setup depends on the slope (through the κ dependency

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as discussed earlier), and the second is that the oscillating wave setup component should depend on the width of the input spectrum. Referring to Fig. 1.6, which is one of several similar plots presented in the Hedges and Mase paper, since each plot may include a mix of beach slopes, the slope dependency is not resolved in the Smean results which of course are derived from the y-intercept of these graphs. Secondly, these experiments were not designed to evaluate the eﬀect of spectral width and the spectral characteristics included in the experiments are not known. However, it is of interest to identify the “representative” κ value and beach slope associated with a

Smean= ηavg/H1_/3of 0.17. Referring to Fig. 1.2, we see that the associated κ value is approximately 0.63 for F0. Based on the Dally et al.8 breaking wave model, the associated beach slope from Fig. 1.3 is 1:29 compared to the beach slopes in the Mase experiments ranging from 1:30 to 1:5.

1.5.2. Field experiments on wave setup

The paragraphs below describe several ﬁeld experiments and observations of wave setup.

An early study of wave setup comprised a pair of observations at an exposed coastal site (Narragansett Pier, RI) and a calmer water site (Newport, RI) where, at the latter, wave action was assumed not a factor and was found to show an approximate 3 foot water level diﬀerence during the peak of the 1938 hurricane storm surge.26

In a second early field experiment on wave setup at Fernandina Beach, Florida, Dorrestein27 _{placed transparent plastic tubes with lightweight floats to track the} water surface on the beach in the zone of wave setup. To obtain the setup records, 16 mm movie film recorded the tracked surface of the floats. A float type tide gage on the end of a fishing pier provided offshore water level records. Through analysis of the tide gage records and the beach placed setup gages, Dorrestein27 evaluated the setup (with respect to the end of the pier) and compared observational results to existing setup theory. He found the measured setup in four of five experiments to be larger than the computed setup. One shortcoming of Dorrestein’s work is that the water level records were only 72 s in length and thus subject to considerable scatter and large standard deviation as later noted by Holman and Sallenger.28 _Although rationale was provided by Dorrestein27 _{for possible differences between measured} and computed setup in this early experiment, large discrepancies between measured and analytically or numerically computed setup still exist today.

A North Sea ﬁeld wave setup experiment was conducted on the Island of Sylt by Hansen.29 _{Utilizing a combination of ultrasonic wave gages and pressure sensor} wave gages out to a distance of 1280 m from shore (10 m depth), Hansen29 _found good correspondence of data to an empirical expression provided by:

η = 0.3Hos= 0.42Horms. (1.15)

Hansen also noted the maximum wave setup to be approximately 50% of the signif-icant breaking wave height. It is not clear as to the methodology utilized to obtain

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Wave Setup 13

A wave setup field experiment was conducted as part of the Nearshore Sed-iment Transport Study at Torrey Pines Beach, San Diego, California by Guza and Thornton.30 _{The Torrey Pines Beach face was gently sloping (beach slope} _{≈ 0.02)} and the beach material was a moderately sorted fine grain sediment (≈ 0.1 mm). A dual wire resistance runup meter was used for the recording and estimation of the wave setup. It should be noted that the measurements of the wave setup were considered to be the average runup determined from wires placed approximately 3 cm above the beach level rather than an actual water level at one location in these experiments. Offshore pressure sensors outside the surf zone at mean depths of 7 to 10.5 m were used for estimating wave height with recording lengths of 4096 s. Guza and Thornton30 _{note specific problems in the data set, which are typical of} field measurements, i.e., the difficulty in obtaining a common datum for the off-shore wave measurements and the beach wave setup measurements. Results of their measurement program suggest an empirical relationship as follows:

η = 0.17Hos= 0.24Horms (1.16)

with scatter that suggests η/Hosranging approximately from 0.05 to 0.50 for indi-vidual experiments.

Holman and Sallenger28_{conducted a field experiment for measuring wave setup} as well as other surf zone parameters at the U.S. Army Corps of Engineers field research pier in Duck, NC, USA. Data on water level at the shoreline were col-lected using longshore looking time lapse photography from Super-8 movie cameras mounted on the research pier scaffolding. The beach at the experiment site had a very steep foreshore (∼ 1 on 10) while the offshore profile slope is much milder (∼ 1 on 100). Beach material was bimodal in size with a median sand size of 0.25 mm and a coarse fraction of 0.75 mm. Results of the experiments showed considerable scatter and dependence on tide level. Regression lines were fit to the data (segmented by tide levels) with results as follows for high tide and mid-tide data:

η

Hs= 0.35ξ0+ 0.14 (high tide) , (1.17)

η

Hs= 0.46ξ0+ 0.06 (mid-tide) . (1.18)

As most of the data fell in a range of ξ0= 1 to 2, the maximum setup was noted to be of the same order as the signiﬁcant wave height in many of the experiments, much higher than theoretically suggested values. Note that in terms of Horms(based on consideration of monochromatic theory results) the setup would be much higher than most other studies show or suggest.

Although Holman and Sallenger28 conclude from their experiments that the setup is dependent on the Iribarren number, it is not entirely clear from their data, especially for higher waves (i.e., see Fig. 1.4, Ref. 28). An additional problem that must be considered when computing the Iribarren number for real beaches and irregular waves is how to deﬁne beach slope. It should be noted that video camera (visual) approaches estimate setup via the measurement of the water surface ele-vation on the beach (similar to the Guza and Thornton measurements) rather than an actual vertically ﬂuctuating water level. The anomaly between dependence of

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setup on Iribarren number as noted by Holman and Sallenger28_{is likely due to the} aforementioned relationship between the wave-breaking coeﬃcient, κ, and beach slope.

Nielsen31and Davis and Nielsen32 conducted a novel setup experiment on Dee Why Beach, in New South Wales, Australia using a set of manometer tubes as shown in Figs. 1.7 and 1.8 from Davis and Nielsen.32_{The tubes were deployed throughout} the beach face and surf zone. A total of 120 setup profiles were measured in 11 days. Wave heights Hormsranged from 0.6 to 2.6 m in height and significant wave periods (T_s) ranged from 5.8 to 12.1 seconds. A shoreline setup of about 40% of Hormswas found although Davis and Nielsen32 _{point out that there is reason to believe that} the surf zone characteristics influence the relationship between wave height and setup magnitude, and also note a problem of defining beach slope via the Iribarren number. Nielsen31_{and Davis and Nielsen}32_{also observe that a major portion of the} setup occurred on the beach face as shown in Fig. 1.9.

Nielsen31 _{points out that previous field investigations have typically measured} the mean water level elevation on the beach as opposed to the average fluctuating mean water level in the vertical plane (i.e., the wave setup as usually defined), and that the two measurements are often different in part due to the beach permeability, which in turn is related to beach material size. The issue of extracting wave setup from runup and rundown on the beach is illustrated in Fig. 1.10.

King et al.33 _{collected wave setup data at Woolacombe Beach in North Devon,} U.K. which faces the North Atlantic Ocean. The beach face slope varied between 1 on 40 at high tide and 1 on 70 at mid-tide level with a tidal range of 3 m at neap and as much as 9 m at springs. Beach face material consisted of ﬁne sand with

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Wave Setup 15

Fig. 1.8. Schematic diagram of apparatus (from Ref. 32).

Fig. 1.9. Dimensionless setup versus total depth where much of the setup occurs on the beach face (from Ref. 32). In this ﬁgure,B and D are equal to η and h as used in this chapter, respectively.

90% in the 0.125 mm to 0.25 mm size range. Pressure transducers were utilized to collect wave and setup information at various stations across the beach and also in a longshore direction to assess the spatial variability of the mean setup. Both tripod mounted and buried pressure transducers were utilized. The buried pressure transducers were 50 to 80 cm below the beach surface and were protected by a porous cover. Instruments collected pressure data which were then transformed to water level data over 4096 second intervals. Data did not include sampling in very shallow water and the maximum wave setup was estimated by extrapolating the

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Fig. 1.10. Illustration of diﬀerences between mean water level (MWL) shoreline and mean water line on beach.

water surface from the most shoreward water stations. Wave setup estimated from the data showed the wave setup to be roughly:

η = 0.10Hos= 0.14Horms (1.19)

with most of the values of η/H_orms between 0.11 and 0.15. The authors do not speculate as to why such low values of setup (compared to analytical results) were found in this measurement program.

Yanagishima and Katoh34 _{discuss field measurements of mean water level near} the shoreline on the Pacific Coast of Japan as measured by an ultrasonic wave gage mounted on a pier where the mean depth of water was ∼ 0.4 m. The setup was determined via a multiple regression approach on 1305 sets of (20 minute records) data taking into account astronomical tide, wind setup, and atmospheric pressure head components of mean water level. Their data included 91 records in which the offshore wave height was above 3 m. Yanagishima and Katoh’s34_{regression analysis} suggested the following relationship:

η = 0.0520Hos _L os Hos 0.2 , (1.20)

which can be formulated in terms of Iribarren number for their beach slope (1 on 60) to the following:

η = 0.27Hos(ξ0)0.4= 0.38Horms(ξ0)0.4. (1.21)

Yanagishima and Katoh34 noted reasonable agreement with the theory of Goda35 (to be discussed later). Even higher values of setup would be expected on the beach face in accord with theory and ﬁndings of other researchers.

Greenwood and Osborne36 conducted field measurements on a Georgian Bay Beach, in Lake Huron, Ontario, Canada. Lake Huron has no measurable tide and the beach profile at the site had a slope of 0.015 with a steeper sloped (0.031 to 0.047) inshore bar. Setup was measured using surface piercing resistance wire wave staffs with the shoreward most gage being in approximately 0.4 m of water depth. Measured setup values were found as follows:

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Wave Setup 17

It is again noted that even higher values of setup would be expected on the beach face in accord with theory and experience of other researchers.

Further work by Hanslow and Nielsen37,38 _{utilized the manometer tube} deployment shown in Fig. 1.7 on three additional beaches (Seven Mile, Palm, and Brunswick) in New South Wales, Australia. With beach face slopes ranging from 0.03 to 0.16 and mean grain sizes of swash zone beach material ranging from 0.18 to 0.5 mm, shoreline beach setup was measured using 20 minute record averages. Using the data from these three beaches as well as earlier measurements at Dee Why Beach (see Refs. 31 and 32), linear least square relationships were ﬁt to the data as follows: η = 0.27Hos= 0.38Horms with R = 0.65 (1.23) or η = 0.040HosL0= 0.048 HormsL0 with R = 0.77 , (1.24)

where a somewhat higher value of explained regression was noted using wave height and wave period. Data and regression lines for these two relationships are shown in Figs. 1.11 and 1.12. The improvement in ﬁt due to inclusion of the deep water wavelength is not evident visually.

A signiﬁcant ﬁnding of these studies was that a major portion of the setup occurred on the beach face (see Fig. 1.9). Further measurements on wave setup at two river entrances is also discussed in Hanslow and Nielsen37 _{and Dunn et al.}39 with the result that the wave setup at river entrances was found to be (somewhat surprisingly) negligible.

Lentz and Raubenheimer40report on a ﬁeld experiment at the U.S. Army Field Research Pier in Duck, NC, USA where 11 pressure sensor gages and 10 sonar altimeters extended across the surf zone from 2 to 8 m of water depth. Close agreement with Longuet-Higgins radiation stress theory for wave setup was noted

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Fig. 1.12. Empirical relationship between setup and wave parameters (from Ref. 38).

although the lack of setup measurements in shallow water (< 2 m) did not allow conclusions regarding the maximum setup that might be expected on the beach.

Raubenheimer et al.41 report on a second ﬁeld experiment at the U.S. Army Field Research Pier in Duck, NC, USA where 12 buried pressure sensor gages were employed across the surf zone from the shoreline to 5 m of water depth. Again good agreement with Longuet-Higgins and Stewart42 radiation stress theory was noted by integration of the cross-shore momentum equation to estimate the wave setup for water depths greater than 1 m but the theory was found to under-predict wave setup in shallow water (h < 1 m). The lack of setup measurements on the beach face did not allow conclusions regarding the maximum setup that might be expected on a beach although an empirical equation was provided to estimate wave setup at the SWL line as follows:

η_SWL

H_os = 0.019 + 0.003βf−1/3, (1.25)

where β_f is the average slope across the surf zone. Raubenheimer et al.41 suggest that theory under-predicts the setup by a factor of 2 for water depths less than 1 m. Stockdon et al.43 _{using video shoreline water level time series determined wave} setup and wave runup results during 10 diverse ﬁeld experiments (four from Duck, NC, USA; four from West Coast beaches in California/Oregon, USA; and two from Terschelling, The Netherlands). These wave setup results were analyzed to provide empirical parameterizations for wave setup under many natural beach conditions as follows:

η = 0.385β_fH0L0, (1.26)

which, assuming that tan β_f ≈ β_f can be expressed in terms of the Iribarren number as

η

H0

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Wave Setup 19

and for extremely dissipative beaches

η

H0

= 0.043

H0/L0

, (1.28)

where H0 is the effective deep water wave height, L0is the deep water wave length associated with the peak spectral period and β_f is the average slope over a depth range defined in terms of the standard deviation of the water surface displacement. It should again be noted that the video camera (visual) approach estimates setup via the mean of measurements of the water surface elevation on the beach rather than the mean of fluctuating water levels at one location.

Results from nine of the field experiments presented here have been analyzed to determine the average ratio of wave setup at the still water line to significant wave height and its associated standard deviation. The ratios at the still water line were determined to be 0.191±0.100. Several caveats apply to these results. In cases where the beach slope and/or the deep water wave steepness was incorporated into the expression presented, these were taken as 0.01 and 0.04, respectively. Some of the published expressions were in terms of the breaking wave height and some in terms of the deep water wave height and no attempt was made to differentiate between breaking and deep water wave heights. The Holman and Sallenger results were not included in these results as they appeared to be anomalously high. Finally, the wave setup ratio at the intersection of the mean water line intersection with the beach profile would be greater than the average ratio (0.191) above. Also, although not examined in detail here, the dynamic wave setup which increases with energetic narrow spectra, would also contribute to the total wave setup.

It is relevant to note that results from ﬁeld measurements are often not con-sistent, possibly due to:

(1) Limited measurement distances across the nearshore.

(2) Use of many diﬀerent approaches to measure/evaluate setup (i.e., videos, pressure sensors, runup gages, manometers, etc.).

(3) Inherent diﬃculties in obtaining a consistent datum for nearshore measurements and oﬀshore measurements.

(4) A clear deﬁnition of setup on the beach face is lacking due to the nature of the permeable beach and the diﬃculty of sub-aerial setup measurements.

1.6. Published Guidance on Wave Setup for Engineering Applications

Several sources of wave setup recommendations are available; two are reviewed here. The U.S. Army Corps of Engineers 1984 Shore Protection Manual (SPM) presents a graphical method to calculate wave setup at mid-depth of the surf zone. This method, developed for irregular waves, is presented in Fig. 1.13 in which the normalized setup has been multiplied by a factor of 2 to transfer approximately the results to the still water shoreline. The eﬀect of beach slope and deep water wave steepness in Fig. 1.13 are evident.

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Fig. 1.13. Nondimensional wave setup versus deep water wave steepness and proﬁle slope by the 1984 Shore Protection Manual recommendations as incorporated in Appendix D of FEMA44 Guidelines. Note that the normalized setup has been multiplied by a factor of 2 to transfer the setup from the mid-depth of the surf zone as it appears in SPM to the approximate still water level contour.Note: S in this ﬁgure is equal to η in this chapter.

Fig. 1.14. Nondimensional wave setup by Goda versus deep water wave steepness and relative water depth within the surf zone. Proﬁle slope = 1:100.

Goda35 has presented guidance for static and dynamic wave setups due to irregular waves. The guidance for static setup and a proﬁle slope of 1:100 is shown in Fig. 1.14. The eﬀects of various deep water wave steepness values are illustrated in Fig. 1.14.

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Wave Setup 21

Table 1.2. Comparison of nondimensional wave setup by SPM and Goda methods for irregular waves. η/H0 H0/L0 SPM Goda 0.005 0.154 0.122 0.01 0.135 0.102 0.02 0.120 0.083 0.04 0.103 0.065 0.08 0.097 0.049

Note: Values in SPM method have been

multi-plied by 2.0 to transfer from surf zone mid-depth to still water line.

Table 1.2 presents a comparison of ratios of nondimensional wave setup values at the still water shoreline as recommended by SPM and Goda. In examining the results in Table 1.2, recall that an additional wave setup occurs from the still water line to the location where the maximum setup intersects the beach proﬁle.

1.7. Summary and Recommendations

The reviews of theory, laboratory and field data, and published guidance for engi-neering applications presented here have identified static and dynamic wave setup components as contributing to the deviation from still water level in the surf zone and their relevance to engineering design. Examination of the static wave setup has reinforced the effect of beach slope on wave setup. The theory presented here does not account for the onshore bottom stress acting on the water column due to undertow.

The available field measurement results exhibit a wide range of wave setup to wave height ratios. Some of this variability is undoubtedly due to the effect of profile slope, which is not accounted for explicitly in some of the analyses and part is due to the effect of wave-breaking in depths greater than the shallow water limit.

Design methodology should account for the static and dynamic wave setup com-ponents. In determining the wave setup to include in design, the characteristics of the particular application of interest should be compared with those of the various ﬁeld and laboratory experiments available including those referenced here. The dom-inant role of beach slope should be recognized. The preliminary results presented here ofη/H_s= 0.191± 0.100 may serve as a useful guide for the static wave setup component.

It is hoped that further research with improved instrumentation, modern sur-veying techniques, and more diverse ﬁeld site studies will help to clarify both the static and dynamic wave setup components for future design applications.

9812819290

edited by

Young C Kim

California State University, Los Angeles, USA

COASTAL AND

OCEAN ENGINEERING

World Scientific

Preface

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Contents

Contributors

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The Editor

Chapter 1

Wave Setup