Inertial Wave Turbulence Driven by Elliptical Instability

Reun, Thomas Le; Favier, Benjamin; Barker, Adrian J.; Bars, Michaël Le

doi:10.1103/physrevlett.119.034502

Cited by 59 publications

(85 citation statements)

References 57 publications

(122 reference statements)

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“…By contrast, we expect it to induce a strong damping of the geostrophic modes, through a drastic increase in bottom drag. In some sense, this honeycomb structure is an experimental means of achieving the specific damping of the geostrophic modes included numerically by Le Reun et al [32]. In line with these expectations, we observe in Fig.…”

Section: Psfrag Replacementssupporting

confidence: 90%

“…Indeed, the relation (4) indicates that this instability sets in when the Ekman number is reduced at fixed Rossby number. The only hope to observe weak wave turbulence is then to focus on distinguished limits where the Rossby number goes to zero faster than some power of the Ekman number [32], the precise boundary in parameter space depending on the dominant damping mechanism (bulk viscosity, Ekman friction, etc.). For wave turbulence to develop, this damping mechanism must be dominant at the quartetic order, but negligible at the triadic one.…”

Section: Psfrag Replacementsmentioning

confidence: 99%

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Shortcut to Geostrophy in Wave-Driven Rotating Turbulence: The Quartetic Instability

2020

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We report on laboratory experiments of wave-driven rotating turbulence. A set of wavemakers produces inertial-wave beams that interact nonlinearly in the central region of a water tank mounted on a rotating platform. The forcing thus injects energy into inertial waves only. For moderate forcing amplitude, part of the energy of the forced inertial waves is transferred to subharmonic waves, through a standard triadic resonance instability. This first step is broadly in line with the theory of weak turbulence. Surprisingly however, stronger forcing does not lead to an inertial-wave turbulence regime. Instead, most of the kinetic energy condenses into a vertically invariant geostrophic flow, even though the latter is unforced. We show that resonant quartets of inertial waves can trigger an instability -the "quartetic instability" -that leads to such spontaneous emergence of geostrophy. In the present experiment, this instability sets in as a secondary instability of the classical triadic instability.

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Section: Psfrag Replacementssupporting

confidence: 90%

Section: Psfrag Replacementsmentioning

confidence: 99%

Shortcut to Geostrophy in Wave-Driven Rotating Turbulence: The Quartetic Instability

2020

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“…As studied in detail by Le Reun et al (2017), the nonlinear saturation of mechanically driven turbulence can give rise either to large-scale structures or to an inertial wave turbulence. It is nevertheless tempting to already extrapolate on the expected magnetic fields, and more specifically on the possibility of obtaining a large-scale magnetic field of interest for planetary applications.…”

Section: Resultsmentioning

confidence: 99%

“…It is nevertheless tempting to already extrapolate on the expected magnetic fields, and more specifically on the possibility of obtaining a large-scale magnetic field of interest for planetary applications. As studied in detail by Le Reun et al (2017), the nonlinear saturation of mechanically driven turbulence can give rise either to large-scale structures or to an inertial wave turbulence. In the former case, the large-scale structures are due to an inverse cascade mechanism from the small-scale patterns excited at the instability onset, as classical in rotating turbulence (see also Barker, 2016b;Barker & Lithwick, 2013a;Lin et al, 2015).…”

Section: Resultsmentioning

confidence: 99%

Turbulent Kinematic Dynamos in Ellipsoids Driven by Mechanical Forcing

Reddy

Favier

Bars

2018

Geophysical Research Letters

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Dynamo action in planetary cores has been extensively studied in the context of convectively driven flows. We show in this letter that mechanical forcings, namely, tides, libration, and precession, are also able to kinematically sustain a magnetic field against ohmic diffusion. Previous attempts published in the literature focused on the laminar response or considered idealized spherical configurations. In contrast, we focus here on the developed turbulent regime and we self‐consistently solve the magnetohydrodynamic equations in an ellipsoidal container. Our results open new avenues of research in dynamo theory where both convection and mechanical forcing can play a role, independently or simultaneously.

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“…In convectively forced rotating turbulence, using experiments with helium performed in a cylinder of aspect ratio 1/2, Ecke and Niemela () find a similar linear scaling for the flux measured through the Nusselt number (normalized by its nonrotating value for the same parameters). Finally, we note that the transition between regimes where either vortices or waves are the dominant modes can be analyzed, in the case of purely rotating flows, in terms of the elliptical instability (Le Reun et al, ). This can justify the presence of turbulence in planetary interiors, which can in turn lead to a dynamo mechanism for the generation of planetary magnetic fields.…”

Section: The Bidirectional or Dual Cascades In Turbulencementioning

confidence: 99%

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Pouquet

Rosenberg

Stawarz

et al. 2019

Earth and Space Science

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We briefly review helicity dynamics, inverse and bidirectional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the nondissipative case, is transferred to small scales through nonlinear mode coupling. Fifty years ago, it was realized that, for a two‐dimensional fluid, energy cascades instead to larger scales and so does magnetic excitation in MHD. However, evidence obtained recently indicates that, in fact, for a range of governing parameters, there are systems for which their ideal invariants can be transferred, with constant fluxes, to both the large scales and the small scales, as for MHD or rotating stratified flows, in the latter case including quasi‐geostrophic forcing. Such bidirectional, split, cascades directly affect the rate at which mixing and dissipation occur in these flows in which nonlinear eddies interact with fast waves with anisotropic dispersion laws, due, for example, to imposed rotation, stratification, or uniform magnetic fields. The directions of cascades can be obtained in some cases through the use of phenomenological arguments, one of which we derive here following classical lines in the case of the inverse magnetic helicity cascade in electron MHD. With more highly resolved data sets stemming from large laboratory experiments, high‐performance computing, and in situ satellite observations, machine learning tools are bringing novel perspectives to turbulence research. Such algorithms help devise new explicit subgrid‐scale parameterizations, which in turn may lead to enhanced physical insight, including in the future in the case of these new bidirectional cascades.

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Inertial Wave Turbulence Driven by Elliptical Instability

Cited by 59 publications

References 57 publications

Shortcut to Geostrophy in Wave-Driven Rotating Turbulence: The Quartetic Instability

Shortcut to Geostrophy in Wave-Driven Rotating Turbulence: The Quartetic Instability

Turbulent Kinematic Dynamos in Ellipsoids Driven by Mechanical Forcing

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

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