Determining Internal Wave Energy Flux from Density Perturbation Measurements

Determination of the internal wave energy flux J=pu in the ocean or atmosphere requires knowledge of the wave perturbation pressure p and velocity u fields, but these fields can rarely be measured. We present a method for determining the velocity, pressure, and energy flux fields for internal waves from the density perturbation field alone. The pressure perturbation field is obtained through a Green's function based analysis, and the velocity field is obtained by manipulating the continuity equation for an incompressible stratified fluid. The method is validated using numerical simulations of the Navier-Stokes equation for a system with an internal wave beam in a fluid with constant buoyancy frequency. The results for the energy flux deduced from density perturbation simulation results agree within a few percent with the flux computed directly in the numerical simulation. The Green’s function method is also applied to density perturbation field laboratory data obtained by the synthetic schlieren technique [Sutherland et al., J. Fluid Mech. 390, 93 (1999)] in our experiment on a stratified fluid in a 3-meter long laboratory tank. The energy flux deduced from the laboratory schlieren measurements agrees within 10% with the flux from the Navier-Stokes simulation. Our method for determining the instantaneous velocity, pressure, and energy flux applies to any system described by a linear approximation of the density perturbation field, e.g., to small amplitude lee waves and propagating vertical modes. The method can be applied using an available Matlab graphical user interface, “EnergyFlux.”