APPENDIX 1

It is of interest to consider the steady state for the simple model in which we disregard the nonlinear advection terms in the three model equations. As seen in Section 3 of the present paper the steady state values of the two wind components and the geopotential may be written as given in (A.1) for an arbitrary n.

Inserting the expressions for u[n] and v[n] from the first two equations in (A.1) in the equation for the geopotential for wave number n we find the result displayed in (A.2).

From the value of the steady state geopotential we may calculate the geostrophic wind component v_g. Taking the ratio of v_g[n] over v[n] we find the result given in (A.3).

It is thus seen that in this simple model we have a good geostrophic adjustment because the frictional coefficient is small compared to the standard value of the Coriolis parameter.