Near-resonant instability of geostrophic modes: beyond Greenspan's theorem

Abstract

Abstract

Mean zonal flows induced by weak mechanical forcings in rotating spheroids

“…2020; Le Reun et al. 2020), where is a typical wavenumber of the flow. On the contrary, boundary-layer interactions establish geostrophic flows on the spin-up time scale .…”

“…Although different in nature, these various scenarios are due to nonlinear bulk interactions and apparently all operate on the dimensionless time scale of order (kRo) −2 in the rapidly rotating planetary regime Ro 1 (e.g. Kerswell 1999;Brunet et al 2020;Le Reun et al 2020), where k is a typical wavenumber of the flow. On the contrary, boundary-layer interactions establish geostrophic flows on the spin-up time scale E −1/2 .…”

Critical transition in fast-rotating turbulence within highly elongated domains

“…A related problem of interest, which we do not address in the present study, is to investigate the transfer of energy to the 2-D manifold in the case when only the 3-D modes are forced. This has recently been studied experimentally and theoretically (Le Reun, Favier & Le Bars 2019; Brunet, Gallet &Cortet 2020, andLe Reun et al 2020).…”

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

“…For nonresonant triads, the contribution of the complex exponential tends toward zero when integrated over times longer than 1/(σ s k + σ s p + σ s q ), strongly reducing the efficiency of the energy exchanges within the triad [26,33]. Although these arguments suggest that only resonant triads are of interest, this is strictly true only at vanishing Rossby number and recent 074801-4 works have shown that nearly resonant [48] and even nonresonant [49] triads can trigger instabilities of inertial waves toward 2D vertically invariant modes at finite Rossby number, these instabilities having however growth rates Ro times smaller than those of the triadic resonance instability.…”