## Numerical Modeling of Ocean DynamicsWhile 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. |

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### Contents

CHAPTER | 1 |

Twodimensional equations | 14 |

Application of the stream function | 22 |

CHAPTER II | 37 |

Boundary and initial conditions | 43 |

Viii | 48 |

Computational and physical modes of the numerical solution | 59 |

Application of the higher order computational schemes | 69 |

Streamfunction models | 319 |

The Bidston models | 328 |

CHAPTER V | 342 |

The normal mode approach | 349 |

Solutions for lakes and bays with uniform and variable depth | 356 |

Systems with branches | 364 |

Resonance calculation for irregularshaped basins | 371 |

Secondary undulations | 378 |

CHAPTER III | 105 |

Numerical solution of the system of equations | 113 |

Twodimensional models | 131 |

CHAPTER IV | 216 |

Threedimensional motion in the shallow seas | 238 |

Threedimensional modeling utilizing the mode splitting | 254 |

General circulation model rigid lid condition | 267 |

T S Murty | 282 |

A twolayer model | 306 |

Quasigeostrophic models | 313 |

Helmholtz mode | 384 |

Numerical models for resonance calculations | 393 |

Kelvin waves Sverdrup waves and Poincare waves | 408 |

STEADY STATE PROCESSES | 414 |

Boundary conditions | 423 |

Direct methods | 435 |

Appendix 1 | 443 |

450 | |

479 | |

### Common terms and phrases

advection equation advective terms algorithm amplitude analytical applied approach assumed average barotropic bottom friction bottom stress boundary condition calculated Ch.II coarse grid coefficients components computational consider constructed continuity equation coordinate Coriolis parameter defined denotes density difference equation diffusion direction domain eddy viscosity energy equation of continuity equation of motion explicit scheme expression finite flux formula free surface frequency friction term given grid point horizontal friction implicit introduced iterative layer leapfrog line inversion method linear long wave matrix nondimensional nonlinear terms normal modes notation numerical diffusion numerical scheme numerical solution obtained ocean open boundary order of approximation parameter phase pressure problem resonance salinity sea level second order seiche solved space step stability staggered grid storm surge stream function stress band Taylor series transport variable vertical velocity vertically integrated water body wave number wind stress zero