Numerical experiments on geostrophic adjustment

A. WIIN NIELSEN

Abstract

The well known geostrophic adjustment problem has been reinvestigated using first a model of a homogeneous atmosphere with a free surface. The basic equations in this model are the two equations of motion for the horizontal velocity components modified to contain only the east-west variations and the continuity equation treated in the same way. A linear frictional term is included in the equations, and the forcing of the model atmosphere is included in the continuity equation. The zonal case is described in Sections 2 and 3. The equations are integrated numerically from an initial state of rest and a horizontal upper surface. If geostrophic adjustment should be obtained, the zonal velocity components should be small, while the meridional velocity components should be in approximate balance with the geostrophic component computed from the zonal geopotential gradient. It is found by integrating the equations for 20 days that the above requirements are satisfied. The numerical integrations of the set of primitive equations are carried out in wave number space, but the results are presented as continuous variations in the west-east directions. It is shown that geostrophic adjustment is reach after a couple of days. The final state of the adjustment process is obtained using several specifications of the forcing. While the final states naturally are different, the geostrophic adjustment is found in each case. A case based on full Fourier series is also included in Section 3. The adjustment problem is also treated in the meridional case in section 4 and 5 using the same strategy as described above. Section 6 contains a solution of the adjustment problem using a two-level, primitive equation model maintaining only the variations in the zonal direction.

Keywords

Geostrophy; adjustment; geostrophic adjustment

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