Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid

Machicoane, Nathanaël; Cortet, Pierre-Philippe; Voisin, Bruno; Moisy, Frédéric

doi:10.1063/1.4922735

Cited by 20 publications

(30 citation statements)

References 39 publications

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“…The apparatus is mounted on a two-meter-diameter platform rotating at a rate Ω = 18 rpm around the vertical axis z. The cylinders oscillate at ω 0 = 0.84 × 2Ω, each cylinder generating four inertial-wave beams [23,25] making angles ± arccos(ω 0 /2Ω) ≃ ±32.9 • with the horizontal [4]. In the central region of the sphere, these beams interact nonlinearly, producing a homogeneous turbulent flow.…”

Section: Psfrag Replacementsmentioning

confidence: 99%

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 Replacementsmentioning

confidence: 99%

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

2020

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“…In Eqs. (6), (7) and (10), the integer m + 1 corresponds to the multipolar order of the line source of waves as discussed in [6]: m = 0 corresponds to a monopolar source and m = 1 to a dipolar source. Our wavemaker produces a large-scale wave with a zero instantaneous net mass flux (because of an integer number of wavelengths) which suggests to consider the dipolar case m = 1.…”

Section: Wave Attractor In the Linear Regime And Beyondmentioning

confidence: 99%

“…These lengthscales (wavelength, beam width) are consequently set by boundary conditions, viscous dissipation and eventually non-linearities. This leads to a variety of wave structures like self-similar wave beams [3][4][5][6], plane waves [7,8] or resonant cavity modes [9][10][11][12][13]. These waves are relevant in geophysics and astrophysics in which they often merge into inertia-gravity waves with a single dispersion relation coupling rotation and buoyancy [2,14].…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear regimes of an inertial wave attractor

2019

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We present an experimental analysis of the linear and non-linear regimes of an attractor of inertial waves in a trapezoidal cavity under rotation. Varying the rotation rate and the forcing amplitude and wavelength, we identify the scaling laws followed by the attractor amplitude and wavelength in both regimes. In particular, we show that the non-linear scaling laws can be well described by replacing the fluid viscosity in the linear model by a turbulent viscosity, a result that could help extrapolating attractor theory to geo/astrophysically relevant situations. We further study the triadic resonance instability of the attractor which is at the origin of the turbulent viscosity. We show that the typical frequencies of the subharmonic waves produced by the instability behaves very differently from previously reported numerical results and from the prediction of the theory of triadic resonance. This behavior might be related to the deviation from horizontal invariance of the attractor in our experiment in relation with the presence of vertical walls of the cavity, an effect that should be at play in all practical situations.

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“…These directions are the characteristics of the hyperbolic equation (2). The details of the structure of the cone depend on the nature of the perturbation [29]. As the dispersion relation does not depend on the wave number (it depends on the direction of k but not on its modulus k), for a given wave frequency there are many (an infinite continuum) of plane wave solutions.…”

Section: Plane Waves Rays and Wave Beamsmentioning

confidence: 99%

Inertial waves in rapidly rotating flows: a dynamical systems perspective

Lopez¹,

Marqués²

2016

Phys. Scr.

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Abstract.An overview of recent developments in a wide variety of enclosed rapidly rotating flows is presented. Highlighted is the interplay between inertial waves, which have been predicted from linear inviscid considerations, and the viscous boundary layer dynamics which result from instabilities as the nonlinearities in the systems are increased. Further, even in the absence of boundary layer instabilities, nonlinearity in the system often leads to complicated interior flows due to subcritical instabilities, Eckhaus bands and heteroclinic dynamics. The ensuing spatio-temporally complex dynamics are analysed in terms of equivariant dynamical systems, providing a general perspective for the wide range of dynamics involved.

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Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid

Cited by 20 publications

References 39 publications

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

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

Linear and nonlinear regimes of an inertial wave attractor

Inertial waves in rapidly rotating flows: a dynamical systems perspective

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