Tidal conversion and turbulence at a model ridge: direct and large eddy simulations

Direct and large eddy simulations are performed to study the internal waves generated by the oscillation of a barotropic tide over a model ridge of triangular shape. The objective is to go beyond linear theory and assess the role of nonlinear interactions including turbulence in situations with low tidal excursion number. The criticality parameter, defined as the ratio of the topographic slope to the characteristic slope of the tidal rays, is varied from subcritical to supercritical values. The barotropic tidal forcing is also systematically increased. Numerical results of the energy conversion are compared with linear theory and, in laminar flow at low forcing, they agree well in subcritical and supercritical cases but not at critical slope angle. In critical and supercritical cases with higher forcing, there are convective overturns, turbulence and significant reduction (as much as 25 %) of the radiated wave flux with respect to laminar flow results. Analysis of the baroclinic energy budget and spatial modal analysis are performed to understand the reduction. The near-bottom velocity is intensified at critical angle slope leading to a radiated internal wave beam as well as an upslope bore of cold water with a thermal front. In the critical case, the entire slope has turbulence while, in the supercritical case, turbulence originates near the top of the topography where the slope angle transitions through the critical value. The phase dependence of turbulence within a tidal cycle is examined and found to differ substantially between the ridge slope and the ridge top where the beams from the two sides cross.