On the Stability of an Intermediate Coupled Ocean-Atmosphere Model

Tianxu Zhao,Guang-An Zou

doi:10.1155/2013/658345

Abstract

The explicit finite difference scheme for solving an intermediate coupled ocean-atmosphere equations has been proposed and discussed. The discrete Fourier analysis within Gerschgorin circle theorem is applied to the stability analysis of this numerical model. The stability criterion that we obtained includes advection, rotation, dissipation, and friction terms, without any assumptions, which is also including the Courant-Friedrichs-Lewy (CFL) condition as a special case. Numerical sensitivity experiments are also carried out by varying the model parameters.

Highlights

The geophysical motions in both the atmosphere and ocean can be described by partial differential equations (PDEs), in recent years, which have become the very popular and important tools in the study of climate change, weather forecasting, and climate prediction
Sensitivity studies are a necessary and important part of the developments of mathematical models of geophysical fluid systems. They can help to reveal aspects of the model that will most profitably benefit from further refinement, as well as providing insights into the fundamental dynamics of these complicated fluid systems [18]
Free-slip boundary conditions in velocity and no-flux boundary conditions in temperature are used in the ocean model

Summary

Introduction

The geophysical motions in both the atmosphere and ocean can be described by partial differential equations (PDEs), in recent years, which have become the very popular and important tools in the study of climate change, weather forecasting, and climate prediction. Both the coupling process of the atmosphere to the ocean and the corresponding PDEs are very complicated; it is almost impossible to find the exact solution of coupled ocean-atmosphere equations. The main purpose of this study is to introduce and solve an intermediate coupled ocean-atmosphere PDEs. The stability analysis of numerical method has been taken into consideration by the discrete Fourier analysis combined with Gerschgorin circle theorem.

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Results

Conclusion