Estimating pressure and internal-wave flux from laboratory experiments in focusing internal waves
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RESEARCH ARTICLE
Estimating pressure and internal‑wave flux from laboratory experiments in focusing internal waves Pierre‑Yves Passaggia1,3,4 · Vamsi K. Chalamalla2 · Matthew W. Hurley1,4 · Alberto Scotti1 · Edward Santilli5 Received: 12 February 2020 / Revised: 24 September 2020 / Accepted: 29 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Graphic abstract
1 Introduction
* Pierre‑Yves Passaggia pierre‑yves.passaggia@univ‑orleans.fr Extended author information available on the last page of the article
Estimating pressure from non-intrusive measurements in fluids is of particular importance in applications such as fluid-structure interaction to determine the forces exerted on structures (Paidoussis 1998), compliant boundaries
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(Wiplier and Ehrenstein 2000), acoustics (Neighbors et al. 1995) and compressible flows (Elsinga et al. 2004). In stratified flows, characteristic of environmental-type flows such as the atmosphere and the oceans, pressure combined with the velocity is directly related to the notion of energy transport and allow for determining the energy flux, a key quantity for computing energy budgets where internal waves drive the dynamics of stratified flows (Kang and Fringer 2012; Rapaka et al. 2013; Jalali et al. 2014) Internal waves are ubiquitous in the ocean. It is now a well-established fact that internal waves play an important role in redistributing the tidal energy in the ocean. Several theoretical studies (Bühler and Muller 2007), observations (Wang and Pawlowicz 2012; Xue et al. 2014), numerical simulations (Duran-Matute et al. 2013), and experimental studies (Shmakova and Flor 2019) investigated the instabilities and breaking of internal waves in various contexts. Another study by Voisin et al. (2011) explored the generation of internal gravity waves by an oscillating sphere using both
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