 # Numerical Modeling of Ocean Dynamics (eBook)

## by ZYGMUNT KOWALIK, T S MURTY(Author)

• 106,466 Words
• 496 Pages

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.

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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