Ocean meso-scale eddy phase speeds in a two-layer quasigeostrophic model

The phase speed spectrum of ocean meso-scale eddies is fundamental to our understanding of turbulent baroclinic flows. Since eddy phase propagation has been shown to modulate eddy fluxes, an understanding of eddy phase speeds is also of practical importance for the development of improved eddy parameterizations for coarse resolution ocean models. However, it is not totally clear whether and how linear Rossby wave theory can be used to explain the phase speed spectra in various weakly turbulent flow regimes. Using linear stability analysis of the two-layer quasigeostrophic model, we identify the theoretical constraints that control the eddy phase speed. We verify these constraints in nonlinear two-layer QG simulations, spanning a range of parameters with potential relevance to the ocean. We find that the strength of the inverse cascade exerts an important control on the eddy phase speed. If the inverse cascade is weak, the phase speed spectrum is reasonably well approximated by the phase speed of the linearly most unstable modes. A significant inverse cascade instead leads to barotropization, which in turn leads to mean phase speeds closer to those of barotropic-mode Rossby waves. Our results are qualitatively consistent with the observed eddy phase speed spectra in the Antarctic Circumpolar Current and may also shed light on the interpretation of phase speed spectra observed in other regimes.