2020
DOI: 10.1017/jfm.2020.454
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Near-resonant instability of geostrophic modes: beyond Greenspan's theorem

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Cited by 21 publications
(24 citation statements)
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“…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 .…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…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 .…”
Section: Discussionmentioning
confidence: 99%
“…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 .…”
Section: Planetary Applicationsmentioning
confidence: 99%
“…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).…”
Section: Quasi-two-dimensionalisation and Inertial Wavesmentioning
confidence: 99%
“…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.…”
Section: Triadic Resonance Of Inertial Wavesmentioning
confidence: 99%