Parametric instability and wave turbulence driven by tidal excitation of internal waves

Reun, Thomas Le; Favier, Benjamin; Bars, Michaël Le

doi:10.1017/jfm.2018.18

Cited by 20 publications

(25 citation statements)

References 82 publications

(111 reference statements)

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“…Their growth rate can be larger than one in our dimensionless units (not shown), because their typical timescale is N −1 0 (rather than Ω −1 s ). Note that these subharmonic instabilities have been reported in local stratified simulations (Le Reun et al 2018).…”

Section: Asymptotic Growth Rate In the Equatorial Planesupporting

confidence: 66%

“…Le Dizès 2000), tidal instability can be generated by parametric resonances of gravito-inertial waves, provided that stratification is strong enough for the considered orbital configuration. This provides a theoretical explanation of the instability mechanism investigated numerically in Le Reun et al (2018).…”

Section: Discussionmentioning

confidence: 54%

“…Le Reun et al (2018) investigated the small-scale turbulence sustained by tides in the regime R ≤ 1, in which vertical viscous shearing is significant. However, radiative interiors are in the opposite regime R 1 (Mathis et al 2018).…”

Section: Stratified Regimes (N 0 /ω S ≥ 1)mentioning

confidence: 99%

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Fossil field decay due to nonlinear tides in massive binaries

Vidal

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ud‐Doula

et al. 2019

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Context. Surface magnetic fields have been detected in 5 to 10% of isolated massive stars, hosting outer radiative envelopes. They are often thought to have a fossil origin, resulting from the stellar formation phase. Yet, magnetic massive stars are scarcer in (close) short-period binaries, as reported by the BinaMIcS (Binarity and Magnetic Interaction in various classes of Stars) collaboration. Aims. Different physical conditions in the molecular clouds giving birth to isolated stars and binaries are commonly invoked. In addition, we propose that the observed lower magnetic incidence in close binaries may be due to nonlinear tides. Indeed, close binaries are probably prone to tidal instability, a fluid instability growing upon the equilibrium tidal flow via nonlinear effects. Yet, stratified effects have hitherto been largely overlooked. Methods. We theoretically and numerically investigate tidal instability in rapidly rotating, stably stratified fluids permeated by magnetic fields. We use the short-wavelength stability method to propose a comprehensive (local) theory of tidal instability at the linear onset, discussing damping effects. Then, we propose a mixing-length theory for the mixing generated by tidal instability in the nonlinear regime. We successfully assess our theoretical predictions against proofof-concept, direct numerical simulations. Finally, we compare our predictions with the observations of short-period, double-lined spectroscopic binary systems. Results. Using new analytical results, cross-validated by a direct integration of the stability equations, we show that tidal instability can be generated by nonlinear couplings of inertia-gravity waves with the equilibrium tidal flow in short-period massive binaries, even against the Joule diffusion. In the nonlinear regime, a fossil magnetic field can be dissipated by the turbulent magnetic diffusion induced by the saturated tidal flows. Conclusions. We predict that the turbulent Joule diffusion of fossil fields would occur in a few million years for several short-period massive binaries. Therefore, turbulent tidal flows could explain the observed dearth of some short-period magnetic binaries.

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Section: Asymptotic Growth Rate In the Equatorial Planesupporting

confidence: 66%

Section: Discussionmentioning

confidence: 54%

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Fossil field decay due to nonlinear tides in massive binaries

Vidal

Cébron

ud‐Doula

et al. 2019

A&A

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“…4(a). The same exponent has been obtained in various numerical simulations with different forcing mechanisms [32,33].…”

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confidence: 67%

Succession of Resonances to Achieve Internal Wave Turbulence

et al. 2020

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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.

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“…a non-linear state made of a superposition of waves in non-linear resonant interaction (Galtier 2003;Bellet et al 2006). This wave turbulence state has been reported in various other contexts such as surface capillary waves (Aubourg & Mordant 2015), vibrating plates (Düring et al 2006;Miquel & Mordant 2011) and internal waves in stratified fluids (Brouzet et al 2016;Le Reun et al 2018). Nevertheless, a clear experimental proof that it exists in rotating fluids undergoing mechanical forcing is still lacking, and the regime of parameters for which it could be observed remains to be determined.…”

Section: Introductionmentioning

confidence: 79%

Experimental study of the nonlinear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence

2019

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In this paper, we present an experimental investigation of the turbulent saturation of the flow driven by parametric resonance of inertial waves in a rotating fluid. In our set-up, a half-meter wide ellipsoid filled with water is brought to solid body rotation, and then undergoes sustained harmonic modulation of its rotation rate. This triggers the exponential growth of a pair of inertial waves via a mechanism called the librationdriven elliptical instability. Once the saturation of this instability is reached, we observe a turbulent state for which energy is injected into the resonant inertial waves only. Depending on the amplitude of the rotation rate modulation, two different saturation states are observed. At large forcing amplitudes, the saturation flow mainly consists of a steady, geostrophic anticyclone. Its amplitude vanishes as the forcing amplitude is decreased while remaining above the threshold of the elliptical instability. Below this secondary transition, the saturation flow is a superposition of inertial waves which are in weakly non-linear resonant interaction, a state that could asymptotically lead to inertial wave turbulence. In addition to being a first experimental observation of a wavedominated saturation in unstable rotating flows, the present study is also an experimental confirmation of the model of Le Reun et al. (2017) who introduced the possibility of these two turbulent regimes. The transition between these two regimes and their relevance to geophysical applications are finally discussed. †

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Parametric instability and wave turbulence driven by tidal excitation of internal waves

Cited by 20 publications

References 82 publications

Fossil field decay due to nonlinear tides in massive binaries

Fossil field decay due to nonlinear tides in massive binaries

Succession of Resonances to Achieve Internal Wave Turbulence

Experimental study of the nonlinear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence

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