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Effluent Transport and Diffusion Models for the Coastal Zone

Effluent Transport and Diffusion Models for the Coastal Zone

D. C. L. Lam, C. R. Murthy, R. B. Simpson

ISBN: 978-1-118-66356-1

Mar 2013, American Geophysical Union

168 pages

Select type: Online Book

Description

Published by the American Geophysical Union as part of the Lecture Notes on Coastal and Estuarine Studies Series, Volume 5.

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.

1 INTRODUCTION  1

1.1 Summary of the monograph  7


2 PARAMETERIZATION OF ADVECTION AND DIFFUSION PROCESSES 9

2.1 Principle of mass conservation: the advection-diffusion transport equation 10

2.2 Horizontal turbulent diffusion processes 17

2.3 Length scale dependent diffusion modelling 32

2.4 Advective flow field 37

3 MATHEMATICAL MODELS WITH ANALYTICAL SOLUTIONS 43

3.1 Steady-state models 44

3.2 Application of analytical models 48

4 MARCHING TECHNIQUE SOLUTIONS FOR STRAIGHT PLUME EQUATIONS: EFFECTS OF SCALE DEPENDENT DIFFUSIVITY 53

4.1 Straight plume with scale dependent diffusion 54

4.2 Parametric identification of eddy diffusivity, an inverse problem 60

4.3 Application to observed data 63

4.4 The marching technique versus fully two-dimensional models: the inclusion of along-flow eddy
diffusivity 70

4.5 Variable grid finite difference methods for a two-dimensional straight plume 73

5 FULLY TWO-DIMENSIONAL COMPUTATIONAL TECHNIQUE FOR STEADY PLUME MODELLING 78

5.1 Boundary treatment 79

5.2 Formation of finite element equations 81

5.3 Computational difficulties associated with strong advection 89

5.4 The computational technique for the scale dependent turbulent diffusivity 98

6 TESTING FINITE ELEMENT PLUME MODELS USING EXAMPLES WITH ANALYTICAL SOLUTIONS 104

6.1 Straight plume case: numerical vs. physical diffusion 105

6.2 A test on convergence of iteration scheme 111

6.3 Skewed plume case: a test on mesh orientation and configuration 114

6.4 Circular plume: the choice of basis functions and refinement of meshes 119

7 VERIFICATION AND APPLICATION 133

7.1 Verification of a bent plume, Bronte, Lake Ontario 134

7.2 Analysis of a waste heat plume and a radioactive tritium patch observed near Pickering, Lake
Ontario 140


7.3 Application of transport model to effluent plume predictions 152

REFERENCES 155

APPENDIX I Notations 162

APPENDIX II Subject Index 166