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.

Whole-field density measurements by Digital Image Correlation

“…This occurred in both measurement techniques, optical and probe. Then (10) would involve taking the square root of a negative number. To prevent this, we set all positive derivatives of the density to zero when calculating the buoyancy frequency.…”

“…The density field can be obtained from the gradients of the density perturbations by solving a Poisson equation. This process requires choosing a priori unknown boundary conditions and the propagation of uncertainties from Synthetic Schlieren-based perturbation density gradients to the perturbation density field calculation [15,16,10].…”

On the optimal window size in optical flow and cross-correlation in particle image velocimetry: application to turbulent flows

“…Meunier & Leweke also showed that a second error source is linked to the image pattern deformation, which decreases the height of the correlation peaks. In order to reduce this effect, the windows in DPIVSoft [27,30,3,29,41] are deformed according to the velocity gradients in an iterative process. The problem of finding a sufficiently reliable starting point for the iteration is solved by applying a Gaussian filter to the images for the first correlation.…”

“…A single experimental snapshot of still particles was used to study the filtering effect of each algorithm. The data-set corresponds to neutrally buoyant PIV particles from Cospehric™, at rest in a stratified salt water tank [29]. The average particle image diameter is 3 px while the mean particle concentration is 0.01 ppp, with the particle concentration measured in Particles Per Pixels (ppp) and defined as:…”

Particle radial velocity and concentration kernels estimation in isotropic grid turbulence experiments of inertialess particles at small separation distances

“…The software Stream Pix 7 was used for data stream acquisition. The image pairs were processed with DPIVSoft-2010 (Meunier & Leweke 2003;Passaggia, Leweke & Ehrenstein 2012;Passaggia et al 2020) by means of interrogation windows with dimensions 64 pixel × 64pixel for the first pass and 32 pixel × 32 pixel for the second pass with 50 % overlap. The spatial resolution is approximately 43.4 μm pixel −1 .…”