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

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  • 1 Goddard Institute for Space Studies, Goddard Space Flight Center, NASA, New York, NY 10025
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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, ΔTe, 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 AzAS, where Az is the available potential energy of the time-averaged zonal mean flow. For n = 3 and moderately large ΔTe and kI−1, the kinetic energy of these waves (Ks) is maintained by the energy conversion AsKs. If ΔTe, or kI−1 is smaller while n=3, kinetic energy is supplied to the quasi-stationary waves by the energy conversion KzKs 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 ΔTe 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 ΔTe 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.

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, ΔTe, 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 AzAS, where Az is the available potential energy of the time-averaged zonal mean flow. For n = 3 and moderately large ΔTe and kI−1, the kinetic energy of these waves (Ks) is maintained by the energy conversion AsKs. If ΔTe, or kI−1 is smaller while n=3, kinetic energy is supplied to the quasi-stationary waves by the energy conversion KzKs 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 ΔTe 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 ΔTe 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.

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