Two-layer quasi-geostrophic waves and turbulence over a meridionally sloping bottom with linear bottom drag

We investigate two-layer quasi-geostrophic (QG) turbulence over a sloping bottom using linear wave mode theory, energy and time scale diagnostics, and potential vorticity (PV) flux spectra. We consider bottom slopes of varying sign and magnitude with the topographic PV gradient aligned with the PV gradient due to background vertical shear. We show that, outside of the tropics, the ocean’s most energetic regions have aligned bottom slopes, and that the topographic PV gradient generally dominates over the planetary PV gradient. In the two-layer QG model, bottom slope effects are shown to be twofold: i) small-to-moderate bottom slopes support topographic wave energization, and ii) moderate-to-large bottom slopes support cascade arrest, jet formation, and surface-intensified baroclinic waves. Somewhat counterintuitively, larger bottom slopes support stronger topographic arrest of nonlinear energy but less energetic topographic waves. Flow over an aligned sloping bottom that supports topographic wave propagation in the same (opposite) direction of the background flow is prograde (retrograde). Retrograde jets act as waveguides, and are persistent and self-maintaining. Interjet momentum flux divergence is important for retrograde jet self maintenance due to topographic suppression of interjet buoyancy fluxes. Prograde jets merge and split in time and space, and act as transient waveguides. For a given bottom slope magnitude, prograde flows have smaller characteristic length scales than retrograde flows. This length scale asymmetry is explained by the Doppler shift of the topographic waves. These results inform both fundamental theory of baroclinic turbulence over a bottom slope and topography-aware parameterizations of ocean eddies.