ON THE COMPUTATIONAL STABILITY OF NUMERICAL SOLUTIONS OF TIME-DEPENDENT NON-LINEAR GEOPHYSICAL FLUID DYNAMICS PROBLEMS

Abstract The satisfactory numerical solution of the equations of fluid dynamics applicable to atmospheric and oceanic problems characteristically requires a high degree of computational stability and accurate conservation of certain statistical moments. Methods for satisfying these requirements are described for various systems of equations typical of low. Mach number fluid dynamics systems, and are investigated in detail as applied to the two-dimensional, inertial-plane equation for conservation of vorticity in a frictionless non-divergent fluid. The conservation and stability properties of the spatial differencing methods devised by A. Arakawa are investigated by means of spectral analysis of the stream function into finite Fourier modes. Any of two classes of linear and quadratie conserving schemes are shown to eliminate the non-linear instability discussed by Phillips, although the “aliasing” error remains. Stability related to the time derivative term is investigated through analytic and numerical so...

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