Advanced Physical Oceanographic Numerical Modelling

This book is a direct result of the NATO Advanced Study Institute held in Banyuls-sur-mer, France, June 1985. The Institute had the same title as this book. It was held at Laboratoire Arago. Eighty lecturers and students from almost all NATO countries attended. The purpose was to review the state of the art of physical oceanographic numerical modelling including the parameterization of physical processes. This book represents a cross-section of the lectures presented at the ASI. It covers elementary mathematical aspects through large scale practical aspects of ocean circulation calculations. It does not encompass every facet of the science of oceanographic modelling. We have, however, captured most of the essence of mesoscale and large-scale ocean modelling for blue water and shallow seas. There have been considerable advances in modelling coastal circulation which are not included. The methods section does not include important material on phase and group velocity errors, selection of grid structures, advanced methods to conservation in highly nonlinear systems, inverse methods and other important ideas for modern ocean modelling. Hopefully, this book will provide a foundation of knowledge to support the growth of this emergent field of science. The NATO Advanced Study Institute was supported by many organi­ zations. The seed money, of course, was received from the NATO Science Commi ttee. Many national organizations provided travel money for partiCipants. In France, CNES, IFREMER, and CNRS provided funds to support the French participants. In the U. S.

Contenu

1.- a. Introduction.- b. Introduction to Ocean Modeling.- c. History and Methodology of Modelling the Circulation of the World Ocean.- 2 Some Useful Mathematical Preliminaries.- 3.- a. The Steady Problem.- b. Advanced Methods for Steady Problems - Direct Elliptic Solvers.- c. Application of Multi-Level Techniques to the Stommel Problem with Irregular Boundaries.- d. A Numerical Approach to Equatorial Oceanic Wave-Mean Flow Interactions.- 4.- a. The Diffusive Problem.- b. Small-Scale Parameterization in Large-Scale Ocean Models.- 5 Time Integration Schemes.- 6 The Hyperbolic Problem.- 7 Finite-Difference Formulation of a World Ocean Model.- 8.- a. Quasigeostrophic Modelling of Eddy-Resolved Ocean Circulation.- b. Periodic Quasi-Geostrophic Models.- 9.- a. Supercomputers in Ocean Modelling.- b. Vector Computers and Vector Programming.- c. Ocean Modelling on Supercomputers.- d. Channel Dynamics and its Application to the Antarctic Circumpolar Current.- 10 Worldwide Ocean Tide Modelling.- 11.- a. Mathematical Formulation of a Spectral Tidal Model.- b. Mathematical Formulation of a Spectral Circulation Model.- 12 Open Boundary Conditions in Numerical Ocean Models.- 13.- a. Data Assimilation.- b. Data Assimilation, Mesoscale Dynamics and Dynamical Forecasting.- c. Sensitivity Studies and Observational Strategies from a Non-Linear Finite-Difference Ocean Circulation Model.- 14.- a. The Treatment of Mixing Processes in Advective Models.- b. About Some Numerical Methods Used in an Ocean General Circulation Model with Isopycnic Coordinates.- c. Towards a Nonlinear 2-Mode Model with Finite Amplitude Topography and Surface Mixed Layer.- d. On the Use of Finite Element Methods for Ocean Modelling.- e. Bottom Stress and Free Oscillations.- Postface.