Nonlinear evolution of the elliptical instability: 
an example of inertial wave breakdown

Mason, Daniel; Kerswell, Rich R.

doi:10.1017/s0022112099005959

Cited by 44 publications

(58 citation statements)

References 38 publications

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“…In some cases, we observed that two pairs of free modes both satisfying the triadic resonance conditions can grow simultaneously. This has been predicted by previous theoretical and numerical studies 38,45 , but, to our knowledge, it is the first experimental evidence. Our experiments have shown that the amplitude of the forced flow does not vary significantly, i.e.…”

Section: Discussionsupporting

confidence: 81%

Experimental study of fluid flows in a precessing cylindrical annulus

2014

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The flow inside a precessing fluid cavity has been given particular attention since the end of the 19th century in geophysical and industrial contexts. The present study aims at shedding light on the underlying mechanism by which the flow inside a precessing cylindrical annulus transitions from laminar to multiple scale complex structures. We address this problem experimentally using ultrasonic Doppler velocimetry to diagnose the fluid velocity in a rotating and precessing cylindrical annulus. When precession is weak, the flow can be described as a superposition of forced inertial modes. Above a critical value of the precession rate, the forced flow couples with two free inertial modes satisfying triadic resonance conditions, leading to the classical growth and collapse. Using a Bayesian approach, we extract the wavenumber, frequency, growth rate and amplitude of each mode involved in the instability. In some cases, we observe for the first time ever experimentally two pairs of free modes coexisting with the forced flow. At larger precession rates, we do not observe triadic resonance any more, instead we observe several harmonics whose frequencies are integer multiples of the rotation frequency.

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Section: Discussionsupporting

confidence: 81%

Experimental study of fluid flows in a precessing cylindrical annulus

2014

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“…The presence or absence of geostrophic modes appears to be important, but the diversity remains to be explained in detail. Indeed, each inertial wave excited by elliptical instability of the base flow can be itself unstable to a triadic resonance with another pair of inertial waves [22]: these secondary instabilities have been observed both numerically [17,23] and experimentally [24]. Whether these multiple resonances asymptotically lead to a wave turbulence regime [25,26], similar to the recently observed regimes with flexural waves in plates [27], gravity-capillary waves [28], and internal waves [29], remains to be seen.…”

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confidence: 75%

Inertial Wave Turbulence Driven by Elliptical Instability

et al. 2017

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The combination of elliptical deformation of streamlines and vorticity can lead to the destabilization of any rotating flow via the elliptical instability. Such a mechanism has been invoked as a possible source of turbulence in planetary cores subject to tidal deformations. The saturation of the elliptical instability has been shown to generate turbulence composed of nonlinearly interacting waves and strong columnar vortices with varying respective amplitudes, depending on the control parameters and geometry. In this Letter, we present a suite of numerical simulations to investigate the saturation and the transition from vortex-dominated to wave-dominated regimes. This is achieved by simulating the growth and saturation of the elliptical instability in an idealized triply periodic domain, adding a frictional damping to the geostrophic component only, to mimic its interaction with boundaries. We reproduce several experimental observations within one idealized local model and complement them by reaching more extreme flow parameters. In particular, a wave-dominated regime that exhibits many signatures of inertial wave turbulence is characterized for the first time. This regime is expected in planetary interiors.

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“…Although it has been demonstrated that the instability ultimately leads to small-scale disorder both experimentally 24 and numerically, 25,26 our theoretical understanding of this process is mostly limited to the initial exponential phase of the instability mechanism. 27 The eventual collapse of the excited inertial modes and the properties of the small-scale flow resulting from it are still not well understood. This turbulent regime in closed geometries has been barely considered mainly for technical reasons: it is difficult to obtain reliable laboratory measurements of the small-scale flow and numerical simulations are rare due to the difficulty in considering a large-scale non-axisymmetric geometry and a small-scale turbulent flow at the same time.…”

Section: Introductionmentioning

confidence: 99%

Generation and maintenance of bulk turbulence by libration-driven elliptical instability

et al. 2015

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Longitudinal libration corresponds to the periodic oscillation of a body’s rotation rate and is, along with precessional and tidal forcings, a possible source of mechanically-driven turbulence in the fluid interior of satellites and planets. In this study, we present a combination of direct numerical simulations and laboratory experiments, modeling this geophysically relevant mechanical forcing. We investigate the fluid motions inside a longitudinally librating ellipsoidal container filled with an incompressible fluid. The elliptical instability, which is a triadic resonance between two inertial modes and the oscillating base flow with elliptical streamlines, is observed both numerically and experimentally. The large-scale inertial modes eventually lead to small-scale turbulence, provided that the Ekman number is small enough. We characterize this transition to turbulence as additional triadic resonances develop while also investigating the properties of the turbulent flow that displays both intermittent and sustained regimes. These turbulent flows may play an important role in the thermal and magnetic evolution of bodies subject to mechanical forcing, which is not considered in standard models of convectively driven magnetic field generation.

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Nonlinear evolution of the elliptical instability: an example of inertial wave breakdown

Cited by 44 publications

References 38 publications

Experimental study of fluid flows in a precessing cylindrical annulus

Experimental study of fluid flows in a precessing cylindrical annulus

Inertial Wave Turbulence Driven by Elliptical Instability

Generation and maintenance of bulk turbulence by libration-driven elliptical instability

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