Tidally-forced flow in a rotating, stratified, shoaling basin

• We propose a mathematical model for tidally driven flow in a shoaling basin.
• A spectrally based numerical model is used to simulate the baroclinic response.
• A tidally driven setup of the isopycnals drives a geostrophic boundary current.
• The cyclonic, subsurface current is baroclinically unstable and spawns eddies.
• The subsurface current is reminiscent of poleward eastern boundary currents.

Baroclinic flow of a rotating, stratified fluid in a parabolic basin is computed in response to barotropic tidal forcing using the nonlinear, non-hydrostatic, Boussinesq equations of motion. The tidal forcing is derived from an imposed, boundary-enhanced free-surface deflection that advances cyclonically around a central amphidrome. The tidal forcing perturbs a shallow pycnocline, sloshing it up and down over the shoaling bottom. Nonlinearities in the near-shore internal tide produce an azimuthally independent ‘set-up’ of the isopycnals that in turn drives an approximately geostrophically balanced, cyclonic, near-shore, sub-surface jet. The sub-surface cyclonic jet is an example of a slowly evolving, nearly balanced flow that is excited and maintained solely by forcing in the fast, super-inertial frequency band. Baroclinic instability of the nearly balanced jet and subsequent interactions between eddies produce a weak transfer of energy back into the inertia-gravity band as swirling motions with super-inertial vorticity stir the stratified fluid and spontaneously emit waves. The sub-surface cyclonic jet is similar in many ways to the poleward flows observed along eastern ocean boundaries, particularly the California Undercurrent. It is conjectured that such currents may be driven by the surface tide rather than by winds and/or along-shore pressure gradients.