Baroclinic Instabilities of the Two-Layer Quasigeostrophic Alpha Model

Abstract

The class of alpha models for turbulence may be derived by applying Lagrangian averaging to the exact fluid equations and then making a closure approximation based on Taylor?s hypothesis of frozen-in fluctuations. This derivation provides a closed expression for the unknown pseudomomentum in the generalized Lagrangian mean theory of Andrews and McIntyre. In the current study, the mean effects of turbulence on baroclinic instability are explored, as determined by the two-layer quasigeostrophic-alpha model in quasigeostrophic (QG) balance. The QG-alpha model is found to lower the critical wavenumber, reduce the bandwidth of instability, and preserve the value of forcing at onset in the baroclinic case. It also preserves the fundamental dependence of baroclinic instability on the gradient of the potential vorticity. These results encourage using the alpha-model approach?based on combining Lagrangian averaging with Taylor?s hypothesis closure approximations?in simulations of global ocean circulation, because this class of turbulence closure models allows Lagrangian-averaged effects of baroclinic instability to be simulated on a coarse mesh.