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

Abstract

We analyze theoretically and experimentally the triadic resonance instability (TRI) of a plane inertial wave in a rotating fluid. Building on the classical triadic interaction equations between helical modes, we show by numerical integration that the maximum growth rate of the TRI is found for secondary waves that do not propagate in the same vertical plane as the primary wave (the rotation axis is parallel to the vertical). In the inviscid limit, we prove this result analytically, in which case the change in the horizontal propagation direction induced by the TRI evolves from $60^{\circ }$ to $90^{\circ }$ depending on the frequency of the primary wave. Thanks to a wave generator with a large spatial extension in the horizontal direction of invariance of the forced wave, we are able to report experimental evidence that the TRI of a plane inertial wave is three-dimensional. The wavevectors of the secondary waves produced by the TRI are shown to match the theoretical predictions based on the maximum growth rate criterion. These results reveal that the triadic resonant interactions between inertial waves are very efficient at redistributing energy in the horizontal plane, normal to the rotation axis.

arXiv commentAccepted for publication in Physical Review Fluids

References in corpus (26)

• Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum
• Instabilities of Internal Gravity Wave Beams
• Critical balance in magnetohydrodynamic, rotating and stratified turbulence: towards a universal scaling conjecture
• Reflexion and Diffraction of Internal Waves analyzed with the Hilbert Transform
• Hamiltonian formalism and the Garrett-Munk spectrum of internal waves in the ocean
• Experimental study of parametric subharmonic instability for internal waves
• Experimental evidence of a triadic resonance of plane inertial waves in a rotating fluid
• Energy spectra of the ocean's internal wave field: theory and observations
• New wave generation
• Non-linear fate of internal wave attractors
• Quantitative experimental observation of weak inertial-wave turbulence
• Resonant Triad Instability in Stratified Fluids
• Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes
• Finite-size effects in parametric subharmonic instability
• Internal wave attractors: different scenarios of instability
• Shortcut to geostrophy in wave-driven rotating turbulence: the quartetic instability
• Experimental study of the non-linear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence
• Inertial waves and modes excited by the libration of a rotating cube
• Succession of resonances to achieve internal wave turbulence
• Linear and nonlinear regimes of an inertial wave attractor
• Viscous spreading of an inertial wave beam in a rotating fluid
• Earth rotation prevents exact solid body rotation of fluids in the laboratory
• Near-resonant instability of geostrophic modes: beyond Greenspan's theorem
• Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid
• Energy-flux vector in anisotropic turbulence: application to rotating turbulence
• Wake of inertial waves of a horizontal cylinder in horizontal translation

Cited by in corpus (4)

• Internal wave turbulence in a stratified fluid with and without eigenmodes of the experimental domain
• Triadic resonant instability in confined and unconfined axisymmetric geometries
• Laboratory observation of internal gravity wave turbulence in a three-dimensional, large-scale facility
• The stability of propagating plane inertial waves in rotating fluids