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

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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 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, ΔT_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_s) is maintained by the energy conversion A_z→A_S, where A_z is the available potential energy of the time-averaged zonal mean flow. For n = 3 and moderately large ΔT_e and k_I⁻¹, the kinetic energy of these waves (K_s) is maintained by the energy conversion A_s→K_s. If ΔT_e, or k_I⁻¹ is smaller while n=3, kinetic energy is supplied to the quasi-stationary waves by the energy conversion K_z→K_s through the topographic forcing, where K_z 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 ΔT_e and 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 ΔT_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.

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