Revisiting the Baroclinic Eddy Scalings in Two-Layer, Quasigeostrophic Turbulence: Effects of Partial Barotropization

Abstract

Abstract In this study, modifications of the Held scaling (Held) are proposed and tested against simulations of f-plane, two-layer quasigeostrophic turbulence. The aim is to better constrain the eddy mixing length and rms barotropic velocity in response to varied quadratic and linear bottom drag. The proposed modifications allow eddies to be partially barotropized, to relax the commonly invoked barotropization approximation, and consider a drag-dependent cascade rate per energy input, to account for the lack of an inertial range. Quantitative comparisons with the vortex gas scaling are also carried out. It is shown that the progressively weakened sensitivity in eddy scales to increased drag strength is mainly a result of eddy partial barotropization. For both drag forms except toward the limit of weak linear drag, accounting for partial barotropization alone leads to good predictions of eddy velocity, although not of mixing length. It also partly resolves the degeneracy of balance constraints for linear drag because partial barotropization acts like scale-dependent damping. Adding a cascade correction, which is interpreted as allowing for changes in spectral room for cascade, further improves the mixing length representation. Overall, the proposed theory can augment the existing scalings by extending the eddy scale predictions to O(1) quadratic drag and has skills generally comparable to the vortex gas scaling for linear drag. However, toward the weak linear drag limit where eddies approach complete barotropization, the proposed theory breaks down but the vortex gas performs well. Potential issues concerning the applicability of vortex gas to this limit are discussed.