Held, I. M., and E. O'Brien, 1992: Quasigeostrophic turbulence in a three-layer model: effects of vertical structure in the mean shear. Journal of the Atmospheric Sciences, 49(19), 1861-1870.

Abstract: A three-layer, horizontally homogeneous, quasigeostrophic model is selected as one of the simplest environments in which to study the sensitivity of baroclinic eddy fluxes in the atmosphere to the vertical structure of the basic-state temperature gradients or vertical wind shears. Eddy statistics obtained from the model are interpreted in terms of linear theory and a modified "baroclinic adjustment" hypothesis. Both linear theory and the baroclinic adjustment construction are found to provide useful predictions for the vertical structure of the eddy potential vorticity flux.

For equal values of the mean vertical shear, eddy fluxes and energies are greater when the shear is concentrated at lower levels (d²U / dz² < 0)than when the shear is concentrated at higher levels (d²U / dz² > 0). Eddy fluxes are more sensitive to lower-than to upper-level mean temperature gradients. This relative sensitivity is a function of g = f² l / (b N²H), where l is the mean vertical shear and H is the depth of the fluid. It is enhanced as g is reduced, as the unstable modes become shallower, until the eddies become almost completely insensitive to the strength of the upper-layer wind for g < 0.5.