A Geometric Perspective on the Modulation of Potential Energy Release by a Lateral Potential Vorticity Gradient

The release of available potential energy by growing baroclinic instability requires the slope of the eddy fluxes to be shallower than that of mean density surfaces, where the amount of energy released depends on both the flux angle and the distance of fluid parcel excursions against the background density gradient. The presence of a lateral potential vorticity (PV) gradient is known to affect the growth rate and energy release by baroclinic instability, but often makes the mathematics of formal linear stability analysis intractable. Here the effects of a lateral PV gradient on baroclinic growth are examined by considering its effects on the slope of the eddy fluxes. It is shown that the PV gradient systematically shifts the unstable modes toward higher wavenumbers and creates a cutoff to the instability at large scales, both of which steepen the eddy flux angle and limit the amount of energy released. This effect may contribute to the severe inhibition of baroclinic turbulence in systems dominated by barotropic jets, making them less likely to transition to turbulence-dominated flow regimes.