Estimating pressure and internal-wave flux from laboratory experiments in focusing internal waves

Abstract

Instantaneous measurements of pressure and wave flux in stratified incompressible flows are presented for the first time using combined time-resolved particle image velocimetry (PIV) and synthetic schlieren (SS). Corrections induced by variations of the refractive index in this strongly density-stratified fluid are also considered. The test case investigated here is a three-dimensional geometry consisting of a Gaussian ring-type topography forced by an oscillating tide representative of geophysical applications. Density and pressure are reconstructed from SS or PIV in combination with linear theories and combined SS-PIV. We perform a direct comparison between the experimental results and three-dimensional direct numerical simulations of the same flow conditions and control parameters. In particular, we show that the estimated velocity or density and the hence wave flux from linear theory solely based on SS or PIV can be flawed in regions of focusing internal waves. We also show that combined measurements of SS and PIV are capable of circumventing these limitations and accurately reproduce the results computed from the DNS.