Calculating Energy Flux in Internal Solitary Waves with an Application to Reflectance

The energetics of internal solitary waves (ISWs) in continuous, quasi-two-layer stratifications are explored using fully nonlinear, nonhydrostatic numerical simulations. The kinetic energy of an internal solitary wave is always greater than the available potential energy, by as much as 30% for the stratifications considered. Because of different spatial distributions of the kinetic and available potential energy densities, however, the fluxes are quite different. The available potential energy flux is found to always exceed the kinetic energy flux, by as much as a factor of 5. The sizes of the various fluxes in the wave pseudoenergy (kinetic plus available potential energy) equation are compared, showing that, while the linear flux term (velocity pressure perturbation) dominates the fluxes, the fluxes of available potential and kinetic energy are significant for large ISWs. Past work on estimating the reflectance (ratio of reflected to incident pseudoenergy flux) associated with internal solitary waves incident on a linearly sloping bottom in laboratory experiments and numerical simulations has incorrectly assumed that the available potential energy flux was equal to the kinetic energy flux. Hence, the sensitivity of reflectance estimates to the way the flux is calculated is investigated. For these low Reynolds number situations, it is found that a correct account of the available potential energy flux reduces the reflectance by as much as 0.1 when the pycnocline is close to the surface.