Once upon time, Henry Stommel was tasked by Harold Sverdrup to provide an explanation for why western boundary currents such as the Gulf Stream are found on the western boundary, not the eastern boundary. The resolution to the problem, appearing in Stommel 1948, was to add a frictional operator into a barotopic vorticity equation. The interplay of friction with asymmetry encoded within the planetary dispersion relation, i.e. westward phase propagation of Rossby waves, provides the explanation: long Rossby waves have a westward group velocity and short Rossby waves have an eastward group velocity. Long waves propagating into the western boundary are reflected into short waves and quickly dissipate there, providing a frictional boundary layer that supports the western boundary current.
This is wonderful, but does not provide intuition about the physical processes behind the mathematical artifice. Nor does this address what you really want to know about friction in a stratified fluid with sloping boundaries. That is the task of this colloquium talk, in which friction for the ocean interior appears as the interaction between internal gravity waves and mesoscale eddies. We reframe a prognostic formulation presented in Muller 1976 that results in an analogue of Boltzman's equation where eddy induced internal wave-stress perturbations are damped using a nonlinear relaxation time scale approximation and ultimately result in an effective viscosity. Relaxation time scales are taken from recent work using wave turbulence techniques for internal gravity waves (Dematteis et al. 2024). Agreement of the prognostic formulation with data from the Local Dynamics Experiment of PolyMode III, circa 1978-1979, is remarkable. With this knowledge and confidence, we then speculate on the role that this coupling plays in mesoscale eddy dynamics in the Southern Recirculation Gyre of the Gulf Stream. In this instance our interest is the potential enstrophy budget, in which enstrophy is the square of the perturbation potential vorticity and, as is total energy, an inviscid invariant. We argue that this nonlinear relaxation effectively provides a local eddy enstrophy damping consistent with potential vorticity flux observations from the Local Dynamics Experiment.
About the speaker:
Kurt Polzin is a Physical Oceanographer at Woods Hole Oceanographic Institution (WHOI) a independent non-profit dedicated to ocean science, technology, education, and communication.
