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

Abstract

We numerically investigate single-layer shallow-water beta-plane quasi-geostrophic turbulence in a doubly periodic domain with emphasis onwavenumber-frequency spectra.We conduct a broad parameter sweep, varying the deformation radius (Ld ), the narrow-band forcing wavenumber (kf), 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 γβin terms of β, Ld, and the energy injection rate. The moderately low γβcase 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 γβcase 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 γβ, a second dispersion relation appears, roughly corresponding to linear waves on a zonal potential vorticity (PV) staircase. At very high γβ, 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 γβsimulations.