Mathematical Modelling of Ocean Circulation

The problems of ocean dynamics present more and more com­ plex tasks for investigators, based on the continuously sophisti­ cation of theoretical models, which are applied with the help of universal and efficient algorithms of numerical mathematics. The present level of our knowledge in the field of mathemat­ ical physics and numerical mathematics allows one to give rather complete theoretical analysis of basic statements of problems as well as numerical algorithms. Our task is to perform such analy­ sis and also to analyze the results of calculations in order to improve our knowledge of the mechanism of large-scale hy­ drological processes occurring in the World Ocean. The new level of numerical mathematics has essentially influenced , the formation of new solution methods of ocean dynamics prob­ lems, among which an important one is the splitting method, which has been already widely practised in various fields of science and engineering. A number of monographs by N. N. Yanenko, A. A. Samarsky, G.!. Marchuk (Rozhdestvensky and Yanenko 1968; Samarsky and Andreyev 1976; Marchuk 1970, 1980b) and others are devoted to the description of this methods. But the methods of the splitting theory require extensive creative work for their application to concrete problems, which are peculiar, as a rule, in problem formulation. The success of the application of these methods is related to the deep understanding of the essence of the described processes. In the last decades fundamental works of Arakawa, K.

Table of Contents:
1 Formulation of the Problem, Transformation of Equations and Elaboration of Ocean Circulation Models.- 1.1 Initial Equations, Their Simplification and Transformations.- 1.2 Diagnostic Sea Current Models.- 1.3 Some Numerical Methods of Solving Simplified Equations of Hydrodynamics.- 2 The Simplest Methods of Difference Approximation and Constructed Equations Solution.- 2.1 The Construction of Difference Grids.- 2.2 The Methods of Approximation and Equation Solutions.- 3 Numerical Methods of Solving Ocean Dynamics Problems.- 3.1 The Construction and Methods of Solving Simplified Problems of Ocean Dynamics.- 3.2 The Operator Representation of the Problem and the Principal Algorithm of the Splitting.- 3.3 The Evolutional Statement of the Problem.- 3.4 The Difference Schemes for the Equations of Motion.- 3.5 The Approximation of Adaptation Equations by Spadai Variables.- 3.6 The Approximation of the Adaptation Equations by Time.- 3.7 The Choice of the Parameters for Approximation in the Simplest Model.- 3.8 The Organization of the Numerical Algorithm.- 4 The Stationary Problems of Ocean Dynamics.- 4.1 The Statement of the Linearized Problem of the Ocean Climatic Condition.- 4.2 The Simplest Model of the Stationary Ocean Currents.- 4.3 The Ocean Dynamics Model, Taking into Account the Wind-Driven Currents.- 4.4 The Difference Operators of the Ocean Dynamics Problem and the Methods of Approximation.- 4.5 The Iterative Processes for Solving the Ocean Dynamics Difference Equations for the Barotropic Component.- 4.6 The Solution of the Difference Equations of the Ocean Dynamics Baroclinic Component.- 4.7 The Modified Iterative Process.- 4.8 The Simplest Model of Ocean Dynamics, Taking into Account the Non-Linear Turbulent Exchange.- 4.9 The Statement of Several Non-Linear Problems.- 4.10 The Problem of Non-Stationary Adjustment of Flow Fields to Atmospheric Disturbances.- 4.11 The Formation of the Thermocline in the Ocean.- 5 The Analysis of the Results of Calculations.- 5.1 On the Results of Diagnostic Calculations of the Currents in Different Oceanic Basins.- 5.2 The World Ocean Surface Topography and the Surface Gradient Currents.- 5.3 The Large-Scale Circulation and Seasonal Variation of the World Ocean Waters.- 5.4 The Hydrodynamic Adjustment of the Ocean Temperature, Salinity, Density and Flow Fields.- 5.5 The Diagnostic Calculations of Flows and the Adjustment of the Hydrological Elements of the North Atlantic.- 5.6 The Diagnostic Calculations of Flow in the Equatorial Belt of the Ocean.- 5.7 The Calculation of Flows in the Black Sea Offshore Zone.- References.