Asymmetric Effects of Topographic Slopes and Bottom Friction on Lagrangian and Eulerian Eddy Diffusivities in Two-Layer QG Flow

Abstract

We investigate how a topographic slope impacts eddy diffusivities in a two-layer quasi-geostrophic model. There are asymmetric effects of retrograde slopes, where the layer interface and the topography tilt in the same direction, and prograde slopes, where the interface and topography tilt in opposite directions. Moreover, there is asymmetry between the upper and lower layer. Steep retrograde slopes suppress the eddy diffusivity in both layers compared to flat or weak slopes. With a strong prograde slope, coherent, long-lived vortices form in the upper layer; as these are surface-trapped, they are not influenced by topography or bottom friction, and the diffusivity in the upper layer is thus relatively unaffected by the slope. In the lower layer, however, the diffusivities decrease with slope magnitude for both prograde and retrograde slopes. We also compare the Lagrangian diffusivity, derived from particle tracking experiments, and the Eulerian diffusivity, based on the flux-gradient relation for potential vorticity (PV). The two values agree in the upper layer, but not in the lower layer. We present a new expression relating Eulerian and Lagrangian diffusivities, and this correctly captures the differences seen in the lower layer. The difference occurs because bottom friction alters the PV along the particle tracks. The results underline the importance of considering both topographic slopes and bottom friction in parametrizations of mesoscale eddy stirring.