Non-hydrostatic effects in supercritical oceanic lee waves

Lee waves occur wherever a steady current with stable stratification interacts with topography. Their generation causes drag on the current. In the ocean, lee waves exist on length scales smaller than the resolution of global ocean circulation models. Their drag thus requires parameterization.

Lee waves are characterized by the dimensionless numbers J=Nh/U and ε=Uk/N, where U and N are the background velocity and buoyancy frequency, and h and k are height and width scales of the bathymetry. For periodic bathymetry of supercritical height (J>O(1)), the lowest layers of the flow become blocked, and the wave drag saturates, allowing for simple parameterization. However, saturation based parameterization considers only one of the two dimensionless numbers.

To diagnose the role of ε in supercritical lee waves, we use idealized numerical simulations of oceanic scale lee waves and study the evolution of the lowest over-topping streamline. We find that after the onset of blocking, the lowest streamline exhibits bounces with horizontal scales of the internal gravity wavelength. To the background flow, these undulations represent ε=1 width bathymetry, which does not cause drag. Blocking thus has an additional non-hydrostatic effect which further reduces lee wave drag.