Wavenumber-frequency analysis of single-layer shallow-water beta-plane quasi-geostrophic turbulence

We numerically investigate single-layer shallow-water beta-plane quasi-geostrophic turbulence in a doubly periodic domain with emphasis on wavenumber-frequency spectra. We conduct a broad parameter sweep, varying the deformation radius (L d ), the narrow-band forcing wavenumber (k f ), and the meridional gradient of the Coriolis parameter ( β ). Out of 54 simulations we present ten in detail spanning slowly propagating vortices to strong jets. We define a nondimensional parameter γ β in terms of β , L d , and the energy injection rate. The moderately low γ β case is characterized by westward propagating coherent vortices and zonal wavenumber-frequency spectra dominated by a nondispersive line (NDL) corresponding to uniform propagation at or near the long-wave Rossby speed. The moderately high γ β case is characterized by jets, and the NDL persists even when there are no coherent vortices. The jets have large meridional excursions (meanders) that propagate westward nearly uniformly at a speed slower than the long-wave Rossby speed. Also at moderately high γ β , a second dispersion relation appears, roughly corresponding to linear waves on a zonal potential vorticity (PV) staircase. At very high γ β , during the slow evolution to a PV staircase, the structure of the linear waves is altered by the small perturbations to a constant potential vorticity gradient. A simple model treating the small perturbation as a sinusoid accurately predicts the meridional wavenumber-frequency spectra in the very high γ β simulations.