Boundary control of potential vorticity injection with oscillating flows

Steady, along-slope currents over a sloping bottom boundary generate cross-slope Ekman flows in a bottom boundary layer that can modify buoyancy distributions. The resulting horizontal buoyancy anomalies balance vertically sheared geostrophic flows that oppose the background flow in a thermal boundary layer. This is the classic Ekman shutdown problem. If the mean flow has lateral variations, a secondary overturning circulation in the depth-cross-slope plane is induced by the convergence and divergence of the Ekman transport. This spin-down process acts to deplete kinetic energy from the interior. The above two processes normally have much shorter timescales than the simple diffusion effect on the bottom boundaries.

In the ocean, along-slope currents exhibit variability over a range of frequencies. Here we study the generation of near-bottom flows over a sloping bottom with an oscillating mean flow. The equations of motion are solved numerically for a range of oscillation frequencies, mean flow amplitudes and bottom slopes. Model results reveal that the oscillating mean flow produces a rectified vertical eddy potential vorticity (PV) flux into the ocean interior, a ‘PV pumping'. The vertical PV flux peaks near the inertial frequency. We discuss whether the vertical eddy PV fluxes explain the influence of tides on observed slope front variability and the formation of vortices over continental shelves.