Numerical modelling of ocean circulation

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NUMERICAL MODELING OF OCEAN DYNAMICS
by Zygmunt Kowalik (Univ. Alaska) & T S Murty (Inst. Ocean Scis.)

While there are several excellent books dealing with numerical analysis and analytical theory, one has to practically sift through hundreds of references. This monograph is an attempt to partly rectify this situation. It aims to introduce the application of finite-difference methods to ocean dynamics as well as review other complex methods. Systematically presented, the monograph first gives a detailed account of the basics and then go on to discuss the various applications. Recognising the impossibility of covering the entire field of ocean dynamics, the writers have chosen to focus on transport equations (diffusion and advection), shallow water phenomena — tides, storm surges and tsunamis, three-dimensional time dependent oceanic motion, natural oscillations, and steady state phenomena. The many aspects covered by this book makes it an indispensable handbook and reference source to both professionals and students of this field.


Contents:
Formulation of the General Equations:
Equations of Motion, Continuity and Diffusion
Two-Dimensional Equations
Application of the Stream Function
Viscosity in the Turbulent Flow
Transport Equations:
Mathematical Rudiments
Boundary and Initial Conditions
Basic Numerical Properties
Explicit Versus Implicit Numerical Schemes
Centered Numerical Schemes
Computational Errors: Diffusion and Dispersion
Computational and Physical Modes of the Numerical Solution
Diffusive Processes
Application of the Higher Order Computational Schemes to the Advective Equation
Two-Dimensional Numerical Models:
Basic Problems
Numerical Solution of the System of Equations
Step by Step Approach to the Construction and Analysis of Simple Numerical Schemes
Two-Dimensional Models
Numerical Filtering
Grid Refinement
Simulation of Long Wave Run-Up
Finite-Differencing of the Time Derivative
Finite-Differencing of the Space Derivative
Treatment of Open Boundaries
Treatment of the Nonlinear Advective Terms
Moving Boundary Models and Inclusion of Tidal Flats
Nested Grids and Multiple Grids
Stretched Coordinates and Transformed Grid Systems
Three-Dimensional Time-Dependent Motion:
Introduction
Numerical Modeling of the Fjord Circulation
Three-Dimensional Motion in the Shallow Seas
Three Dimensional Modeling Utilizing the Mode Splitting and Sigma Coordinate
General Circulation Model — Rigid Lid Condition
A Three-Dimensional Semi-Implicit Model
A Two-Layer Model
Mode Splitting and Reduced Gravity Model
Quasi-Geostrophic Models
Streamfunction Models
The Bidston Models
Haidvogel et al.'s Model
Normal Modes:
Introduction
Seiches
The Normal Mode Approach
Solutions for Lakes and Bays with Uniform and Variable Depth
Systems with Branches
Resonance Calculation for Irregular-Shaped Basins
Secondary Undulations
Helmholtz Mode
Open Boundary Conditions
Numerical Models for Resonance Calculations
Kelvin Waves, Sverdrup Waves and Poincaré Waves
Influence of Ice Cover on Normal Modes
Steady State Processes:
Oceanographic Examples
Numerical Approximation
Boundary Conditions
Numerical Methods
Direct Methods
Higher Order Accuracy Schemes for Convection-Dominated Flow
Appendix 1
References
Subject Index

Readership: Oceanographers, coastal engineers and environment scientists.

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