Evanescent to propagating internal waves in experiments, simulations, and linear theory

Abstract

Experiments, numerical simulations, and linear theory are used to explore the kinetic energy density of waves generated by oscillating topography in a nonlinear stratification. Initially, generated waves are evanescent but then pass through a turning depth and into a propagating region. A technique for calculating kinetic energy density indirectly via the density perturbation field measured using synthetic schlieren is tested to assess the validity of the calculation. To establish the indirect calculation’s range of validity, numerical simulations were performed to compare the indirect calculation to an estimate of kinetic energy calculated from local velocity components (referred to here as the standard calculation). In addition, the standard calculation is applied to the velocity field determined via linear theory, which defines the fluid velocity using similar assumptions to the indirect calculation of kinetic energy. Both calculation methods show similar trends in the average kinetic energy density present in propagating waves as a function of Froude number, topography height, and distance from topography to the turning depth. Local comparisons of kinetic energy density from the indirect and standard calculations identify regions where the two methods compare well. Additionally, a correlation between linear theory and numerical simulations is presented to evaluate the range of applicability of the linear theory.