Parameterization of gravity current entrainment for ocean circulation models using a high-order 3D nonhydrostatic spectral element model

Building on the work by Turner [Turner, J.S., 1986. The development of the entrainment assumption and its application to geophysical flows. J. Fluid Mech. 173, 431–471] and Hallberg [Hallberg, R., 2000. Time integration of diapycnal diffusion and Richardson number dependent mixing in isopycnal coordinate ocean models. Mon. Weather Rev. 128, 1402–1419], an algebraic parameterization of the entrainment process in gravity current has been derived for isopycnic coordinate ocean models. It casts the entrainment into layers as a function of the layer Richardson number (Ri) times the velocity difference across layers. In order to determine the function f(Ri), simulations of generic gravity currents over various bottom slope angle are conducted with the HYbrid Coordinate Ocean Model (HYCOM) and compared to similar experiments with the high-resolution, three-dimensional, nonhydrostatic model Nek5000, which serves as ground truth. A simple linear function, E = 0.20(1 − Ri/0.25), is found to reproduce quite well the entrainment, salt flux, Richardson number, velocity profile and plume propagation speed in Nek5000. The parameterization is then applied to a realistic-topography simulation of the Mediterranean outflow with HYCOM and shown to produce realistic equilibration depth and water mass properties of the outflow plume.