Energy budget in internal wave attractors experiment

TL;DR

This experimental study investigates the energy budget of internal wave attractors in stratified fluids, quantifying energy fluxes and dissipation in linear and nonlinear regimes without adjustable parameters, and highlighting boundary layer effects.

Contribution

The paper introduces a comprehensive method to measure and analyze energy budgets in internal wave attractors, including boundary layer dissipation and nonlinear effects, with no adjustable parameters.

Findings

Energy budget is closed in linear regime with boundary layer dissipation.

Boundary layer dissipation depends on the set-up thickness.

Secondary waves from triadic resonances transfer energy to smaller scales.

Abstract

The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a \ch{two-dimensional, two components,} experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers are estimated using the theoretical expression of the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech. 841, 614 (2018)). In the linear regime, we show that the energy budget is closed, in the steady-state and also in the transient regime, by taking into account the bulk dissipation and, more important, the dissipation in the boundary layers without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi two-dimensional stratified flow.