Energy budget in internal wave attractor experiments

Abstract

The current paper presents an experimental study of the energy budget of a twodimensional 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 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.

Vortex cluster arising from an axisymmetric inertial wave attractor

“…2020), and such a cascade reaches a statistically steady state when a balance is established between the injected and dissipated energy (Jouve & Ogilvie 2014; Davis et al. 2019). This is to be put in context with some recent development on the understanding of inertial wave turbulence in rotating flows (see, for example, the recent works of Le Reun, Favier & Le Bars (2019) and Brunet, Gallet & Cortet (2020) on the competition between the saturation of rotating turbulence in three-dimensional (3-D) wave turbulence and in -D geostrophic turbulence).…”

Succession of Resonances to Achieve Internal Wave Turbulence

“…The IWA can be seen as a limit cycle, a prominent word in nonlinear physics, which arises from linear theory. Different angles of propagation set by different forcing frequencies lead to different attractors with simple or more complicated shapes: the dashed lines in Figs [24,25]. The energy concentration, which is large just after focusing upon reflection from the slope, is progressively dissipated along the length of the attractor before being focused again by the slope.…”

On (n,1) Wave Attractors: Coordinates and Saturation Time

“…In Figure 3 one can see the typical field of vertical velocity after a (1,1) attractor has established together with the evolution of the total kinetic energy. The details of numerical simulation will be covered in Section 4, the parameters correspond to the laboratory experiments with the wavemaker located at the vertical wall as in [8,27]. The total kinetic energy E is normalized by the maximum kinetic energy of the wave maker oscillating at amplitude a in Equation (1).…”