Maintenance of Quasi-Stationary Waves in a Two-Level Quasi-Geostrophic Spectral Model with Topography

Abstract

The maintenance of the quasi-stationary waves obtained through numerically integrating a two-level quasi-geostrophic spectral model on a ?-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 2n 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, ?Te, and the reciprocal of the internal frictional coefficient, 0.5 kI?1. If the flow is not highly irregular, the available potential energy of quasi-stationary waves (As) is maintained by the energy conversion Az?AS, where Az is the available potential energy of the time-averaged zonal mean flow. For n = 3 and moderately large ?Te and kI?1, the kinetic energy of these waves (Ks) is maintained by the energy conversion As?Ks. If ?Te, or kI?1 is smaller while n=3, kinetic energy is supplied to the quasi-stationary waves by the energy conversion Kz?Ks through the topographic forcing, where Kz 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 n=2 with relatively small ?Te and kI?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 ?Te and kI?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.