Numerical Modeling of Ocean Dynamics
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 DiffusionTwo-Dimensional EquationsApplication of the Stream FunctionViscosity in the Turbulent FlowTransport Equations:Mathematical RudimentsBoundary and Initial ConditionsBasic Numerical PropertiesExplicit Versus Implicit Numerical SchemesCentered Numerical SchemesComputational Errors: Diffusion and DispersionComputational and Physical Modes of the Numerical SolutionDiffusive ProcessesApplication of the Higher Order Computational Schemes to the Advective EquationTwo-Dimensional Numerical Models:Basic ProblemsNumerical Solution of the System of EquationsStep by Step Approach to the Construction and Analysis of Simple Numerical SchemesTwo-Dimensional ModelsNumerical FilteringGrid RefinementSimulation of Long Wave Run-UpFinite-Differencing of the Time DerivativeFinite-Differencing of the Space DerivativeTreatment of Open BoundariesTreatment of the Nonlinear Advective TermsMoving Boundary Models and Inclusion of Tidal FlatsNested Grids and Multiple GridsStretched Coordinates and Transformed Grid SystemsThree-Dimensional Time-Dependent Motion:IntroductionNumerical Modeling of the Fjord CirculationThree-Dimensional Motion in the Shallow SeasThree Dimensional Modeling Utilizing the Mode Splitting and Sigma CoordinateGeneral Circulation Model — Rigid Lid ConditionA Three-Dimensional Semi-Implicit ModelA Two-Layer ModelMode Splitting and Reduced Gravity ModelQuasi-Geostrophic ModelsStreamfunction ModelsThe Bidston ModelsHaidvogel et al.'s ModelNormal Modes:IntroductionSeichesThe Normal Mode ApproachSolutions for Lakes and Bays with Uniform and Variable DepthSystems with BranchesResonance Calculation for Irregular-Shaped BasinsSecondary UndulationsHelmholtz ModeOpen Boundary ConditionsNumerical Models for Resonance CalculationsKelvin Waves, Sverdrup Waves and Poincaré WavesInfluence of Ice Cover on Normal ModesSteady State Processes:Oceanographic ExamplesNumerical ApproximationBoundary ConditionsNumerical MethodsDirect MethodsHigher Order Accuracy Schemes for Convection-Dominated FlowAppendix 1ReferencesSubject IndexReadership: Oceanographers, coastal engineers and environment scientists.
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