Coastal and Estuarine

Transcription

1 Lecture Notes on Coastal and Estuarine Studies Managing Editors: Richard T. Barber Malcolm J. Bowman Christopher N.K. Mooers Bernt Zeitzschel 5 D.C. L.Lam C. R. Murthy R. B. Simpson Effluent Transport and Diffusion Models for the Coastal Zone Springer-Verlag New York Berlin Heidelberg Tokyo 1984

2 Managing Editors Richard T. Barber Duke University Marine Laboratory Beaufort, NC 28516, USA Christopher N. K. Mooers Dept. of Oceanography Naval Postgraduate School Monterey, CA 93940, USA Malcolm J. Bowman Marine Sciences Research Center, State University of New York Stony Brook, NY 11794, USA Bernt Zeitzschel Institut fur Meereskunde der Universitat Kiel Dusternbrooker Weg 20, D-2300 Kiel, FRG Contributing Editors Ain Aitsam (Tallinn, USSR) Larry Atkinson (Savannah, USA) Robert C. Beardsley (Woods Hole, USA) Tseng Cheng-Ken (Tsingtao, PRC) Keith R. Dyer (Taunton, UK) Jon B. Hinwood (Melbourne, AUS) Jorg Imberger (Western Australia, AUS) Hideo Kawai (Kyoto, Japan) Paul H. LeBlond (Vancouver, CAN) Akira Okubo (Stony Brook, USA) William S. Reeburgh (Fairbanks, USA) David A. Ross (Woods Hole, USA) S. Sethuraman (Raleigh, USA) John H. Simpson (Menai Bridge UK) Absornsuda Siripong (Bangkok, Thailand) Robert L. Smith (Corvallis, USA) Mathias Tomczak (Hobart, AUS) Paul Tyler (Swansea, UK) Authors D.C.L. Lam C.R. Murthy National Water Research Institute Canada Centre for Inland Waters Burlington, Ontario L7R 4A6, CAN R.B. Simpson Computer Science Department University of Waterloo Waterloo, Ontario N2L 3G1, CAN Library of Congress Cataloging in Publication Data Lam, D. C. L. Effluent transport and diffusion models for the coastal zone. (Lecture notes on coastal and estuarine studies ; 5) Bibliography: p. Includes index. 1. Sewage disposal in rivers, lakes, etc. Mathematical models. 2. Plumes (Fluid dynamics) Mathematical models. 3. Diffusion Mathematical models. I. Murthy, C. R. II. Simpson, R. B. III. Title. IV. Series. TD763.L '68' by Springer-Verlag New York Inc. All rights reserved. No part of this book may be translated or reproduced in any form without permission from Springer-Verlag, 175 Fifth Avenue, New York, NY 10010, USA. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Printed and bound by Halliday Lithograph, West Hanover, Massachusetts. Printed in the United States of America ISBN ISBN Springer-Verlag New York Berlin Heidelberg Tokyo Springer-Verlag Berlin Heidelberg New York Tokyo Copyright American Geophysical Union. Transferred from Springer-Verlag in June 1992.

3 PREFACE The purpose of this monograph is to summarize the present modelling capability of simulating the transport and dispersion of effluents in the coastal zone regimes of lakes and oceans. It is recognized that the modelling capability strongly depends on the knowledge of the physical processes acquired through theoretical and experimental investigations, and also on the development of computational methods with which these processes can be simulated efficiently and accurately. Our emphasis, therefore, is based on a critical review of several environmental turbulence models which have been directly derived from existing theories and oceanic and limnological data. The search for the computational method is then essentially limited to those which are consistent and adaptive to the theoretical results and the empirical knowledge. Through theoretical analyses and numerical examples, the monograph is intended to provide the necessary background, particularly the successes and pitfalls of interfacing different computational methods and physical models, for investigators of water quality problems and other practical multidisciplinary concerns in the coastal zones. Specifically, the monograph aims at describing the important physical and mathematical aspects towards developing a general computer package which will be capable of simulating different environmental scenarios of effluent discharges. Within this specific scope, emphasis is placed on bridging the gap of knowledge in the fields of geophysical, engineering, environmental and mathematical sciences. Thus, it is unavoidable that parts of the monograph may appear complicated to some readers but trivial to others. Indeed, part of the challenge of writing up the monograph is in trying to maintain some form of knowledge transfer among the individual scientific disciplines. It is hoped that the monograph will lead to, in a limited scope, an improved dialogue among the many diverse disciplines.

4 ACKNOWLEDGEMENTS The authors thank Drs. M.J. Bowman and A. Okubo for providing useful comments, Dr. J.A. George for assistance in the design of the finite element code, K.C. Miners and J.A. Bull for preparation of the experimental data, J. Hodson for computer programming, C. Minnie for typing the manuscript, J. Arda for pre-publication editing, and W. Finn and his staff for drafting the figures. One of the authors (RBS) was supported in part by a research contract from Environment Canada (DSS No. 03SU.KL ).

5 CONTENTS 1 INTRODUCTIO N 1.1 Summary of the monograph Page PARAMETERIZATIO N O F ADVECTION AN D DIFFUSIO N PROCESSE S Principle of mass conservation: the advection-diffusion transport equation Horizontal turbulent diffusion processes Empirical results from dye patch experiments Empirical results from dye plume experiments Length scale dependent diffusion modelling Advective flow field 37 3 MATHEMATICAL MODEL S WIT H ANALYTICA L SOLUTION S Steady-state models Application of analytical models 48 4 MARCHIN G TECHNIQU E SOLUTION S FO R STRAIGH T PLUM E EQUATIONS: EFFECT S O F SCAL E DEPENDEN T DIFFUSIVIT Y Straight plume with scale dependent diffusion Parametric identification of eddy diffusivity, an inverse problem Application to observed data The marching technique versus fully two-dimensional models: the inclusion of along-flow eddy diffusivity Variable grid finite difference methods for a two-dimensional straight plume 73

6 viii Page 5 FULL Y TWO-DIMENSIONA L COMPUTATIONA L TECHNIQU E FO R STEAD Y PLUME MODELLIN G Boundary treatment Formation of finite element equations Computational difficulties associated with strong advection Cell Reynolds number Method instability and upwinding The effects of advection on the matrix of the discrete equations The computational technique for the scale dependent turbulent diffusivity Computing the diffusion tensor TESTIN G FINIT E ELEMEN T PLUM E MODEL S USIN G EXAMPLE S WIT H ANALYTICAL SOLUTION S Straight plume case: numerical vs. physical diffusion A test on convergence of iteration scheme Skewed plume case: a test on mesh orientation and configuration Circular plume: the choice of basis functions and refinement of meshes VERIFICATIO N AN D APPLICATIO N Verification of a bent plume, Bronte, Lake Ontario Analysis of a waste heat plume and a radioactive tritium patch observed near Pickering, Lake Ontario 140

7 IX Page Data analysis Model application Observed and computed results Application of transport model to effluent plume predictions 152 REFERENCES 155 APPENDIX I Notations 162 APPENDIX II Subject Index 166