Baroclinic instability and eddy tracer transport across sloping bottom topography: How well does a modified Eady model do in primitive equation simulations?

Theoretical tracer diffusivities given by linear Eady theory that accounts for non-zero bottom slopes are compared with diffusivities diagnosed from primitive equation simulations of thermally forced flows over an idealized continental slope. The behavior is discussed in terms of a bottom slope parameter δ ¯ , the ratio of the bottom slope to an expression roughly representing the depth-averaged isopycnal slope. The theoretical diffusivities, scaled by the total thermal wind shear and the first internal deformation radius, agree qualitatively with diagnosed diffusivities for δ ¯ ≲ 0 , the parameter regime appropriate for buoyant boundary currents flowing over continental slopes. But whereas Eady theory would suggest maximum diffusivities for moderate positive slopes, δ ¯ ≃ 0.5 , the diagnosed diffusivities are highest for δ ¯ = 0 , i.e. for flat bottoms. Finally, whereas Eady diffusivities should drop to zero for δ ¯ ≳ 1 , i.e. when the bottom becomes steeper than the mean isopycnal slope, the diagnosed diffusivities do not. Similarities and differences are discussed in terms of more general linear stability theory applied to the background density profile over the central slope region. It is found that interior potential vorticity gradients, neglected by Eady theory, both cause significant modification to the Eady mode and also enable non-Eady instabilities that are responsible for the non-zero diffusivities for δ ¯ ≳ 1 . Furthermore, estimates of kinetic energy spectral fluxes suggest that an inverse kinetic energy cascade is present, and it is speculated that this is responsible for the diagnosed maximum diffusivity for flat bottoms.