## Abstract

The maintenance of the quasi-stationary waves obtained through numerically integrating a two-level quasi-geostrophic spectral model on a β-plane is studied. An idealized topography which has only wave-number *n* in the zonal direction and the first mode in the meridional direction is used to force the quasi-stationary waves. However, the model's motion contains wavenumbers 0, *n* and 2*n* in the zonal direction, while the first three modes in the meridional direction are allowed for each wave. The cases *n* = 2 and *n* = 3 are considered.

The mechanism for maintaining the quasi-stationary waves is investigated by varying the imposed thermal equilibrium temperature gradient, Δ*T _{e}*, and the reciprocal of the internal frictional coefficient, 0.5

*k*

_{I}^{−1}. If the flow is not highly irregular, the available potential energy of quasi-stationary waves (

*A*) is maintained by the energy conversion

_{s}*A*→

_{z}*A*, where

_{S}*A*is the available potential energy of the time-averaged zonal mean flow. For

_{z}*n*= 3 and moderately large Δ

*T*and

_{e}*k*

_{I}^{−1}, the kinetic energy of these waves (

*K*) is maintained by the energy conversion

_{s}*A*→

_{s}*K*. If Δ

_{s}*T*, or

_{e}*k*

_{I}^{−1}is smaller while

*n*=3, kinetic energy is supplied to the quasi-stationary waves by the energy conversion

*K*→

_{z}*K*through the topographic forcing, where

_{s}*K*is the kinetic energy of the time-averaged zonal mean flow. The latter mechanism also maintains the kinetic energy of the quasi-stationary waves for

_{z}*n*=2 with relatively small Δ

*T*and

_{e}*k*

_{I}^{−1}is sufficiently large, the flow is highly irregular and a unique regime cannot be defined for either

*n*= 2 or

*n*= 3.

In the case of *n* = 3 and moderately large Δ*T _{e}* and

*k*

_{I}^{−1}, the energy cycle, spectra and form of the quasi-stationary waves suggest that the quasi-stationary waves are largely baroclinic waves which draw their energy from the forced waves.