Succession of Resonances to Achieve Internal Wave Turbulence

Abstract

We study experimentally the interaction of nonlinear internal waves in a stratified fluid confined in a trapezoidal tank. The setup has been designed to produce internal wave turbulence from monochromatic and polychromatic forcing through three processes. The first is a linear transfer in wavelength obtained by wave reflection on inclined slopes, leading to an internal wave attractor which has a broad wave number spectrum. Second is the broadbanded time-frequency spectrum of the trapezoidal geometry, as shown by the impulse response of the system. The third one is a nonlinear transfer in frequencies and wave vectors via triadic interactions, which results at large forcing amplitudes in a power law decay of the wave number power spectrum. This first experimental spectrum of internal wave turbulence displays a k −3 behavior.

Downscale energy fluxes in scale-invariant oceanic internal wave turbulence

“…The quadratic nonlinearity in the primitive fluid equations and a dispersion relation allowing for three-wave interactions imply that internal waves interact through triads. In a weakly nonlinear regime, three-wave resonant interactions are responsible for slow, net energy transfers between different wavenumbers (Davis et al 2020). This process can be described by a wave kinetic equation, the evolution equation of the action spectrum of the internal wave field (Hasselmann 1966;Zakharov, L'vov & Falkovich 1992;Nazarenko 2011).…”

“…In a weakly nonlinear regime, three-wave resonant interactions are responsible for slow, net energy transfers between different wavenumbers (Davis et al. 2020). This process can be described by a wave kinetic equation, the evolution equation of the action spectrum of the internal wave field (Hasselmann 1966; Zakharov, L'vov & Falkovich 1992; Nazarenko 2011).…”

Vortex cluster arising from an axisymmetric inertial wave attractor

“…2016 a , 2017 a ; Davis et al. 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).…”

Three-dimensionality of the triadic resonance instability of a plane inertial wave

“…In this context, wave turbulence theory (WTT), which addresses the statistical properties of weakly nonlinear ensembles of waves in large domains [24][25][26], stands as an interesting direction for improving turbulence parametrizations in coarse atmospheric and oceanic models [27]. This is particularly the case since several recent studies have given credence to the WTT framework for inertial waves in experiments [28] and in numerical simulations [29,30] as well as for internal gravity waves in experiments [31,32].…”