Turbulence and columnar vortex formation through inertial-wave focusing

Duran‐Matute, Matias; Flór, Jan‐Bert; Godeferd, Fabien S.; Jause-Labert, Clément

doi:10.1103/physreve.87.041001

Cited by 22 publications

(25 citation statements)

References 14 publications

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“…TRI) internal wave phenomena in axisymmetric geometries. For example, a recent study by Duran-Matute et al [24] has used focusing by an oscillating torus to study the onset of instabilities; the vertical mode geometry we have developed and demonstrated here provides an arguably even more canonical configuration in which to study such non-linear phenomena, since any axisymmetric wave field can be expressed in terms of Bessel functions.…”

Section: Conclusion and Discussionmentioning

confidence: 95%

“…The amplitude decrease and the viscous decay of the conical wave beam emitted by an oscillating sphere has been explored in laboratory experiments by Flynn et al [17] showing good agreement with theoretical predictions. More sophisticated axisymmetric experimental geometries have been investigated using a vertically oscillating torus [24,25], in which case a highly non-linear process occurs due to the three-dimensional geometric focusing, able to transport momentum and break into turbulence. None of these experimental configurations, however, readily permitted a change in the form nor the wave number of the wave field being excited.…”

Section: Introductionmentioning

confidence: 99%

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Excitation and resonant enhancement of axisymmetric internal wave modes

2019

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To date, axisymmetric internal wave fields, which have relevance to atmospheric internal wave fields generated by storm cells and oceanic near-inertial wave fields generated by surface storms, have been experimentally realized using an oscillating sphere or torus as the source. Here, we use a novel wave generator configuration capable of exciting axisymmetric internal wave fields of arbitrary radial form to generate axisymmetric internal wave modes. After establishing the theoretical background for axisymmetric mode propagation, taking into account lateral and vertical confinement, and also accounting for the effects of weak viscosity, we experimentally generate and study modes of different order. We characterize the efficiency of the wave generator through careful measurement of the wave amplitude based upon group velocity arguments. This established, we investigate the ability of vertical confinement to induce resonance, identifying a series of experimental resonant peaks that agree well with theoretical predictions. In the vicinity of resonance, the wave fields undergo a transition to non-linear behaviour that is initiated on the central axis of the domain and proceeds to erode the wave field throughout the domain.

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Section: Conclusion and Discussionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Excitation and resonant enhancement of axisymmetric internal wave modes

2019

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“…In rapidly rotating 3-D fluids, the energy from inertia waves is transferred towards the quasi-geostrophic mode (Smith and Waleffe, 1999;Cambon et al, 2004;Staplehurst et al, 2008;Duran-Matute et al, 2013).…”

Section: Anisotropic Inverse Cascadementioning

confidence: 99%

The Rossby wave extra invariant in the dynamics of 3-D fluid layers and the generation of zonal jets

Balk

2014

Nonlin. Processes Geophys.

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Abstract.We consider an adiabatic-type (approximate) invariant that was earlier obtained for the quasi-geostrophic equation and the shallow water system; it is an extra invariant, in addition to the standard ones (energy, enstrophy, momentum), and it is based on the Rossby waves. The presence of this invariant implies the energy transfer from small-scale eddies to large-scale zonal jets.We show that this extra invariant can be extended to the dynamics of a three-dimensional (3-D) fluid layer on the beta plane. Combined with the investigation of other researchers, this 3-D extension implies enhanced generation of zonal jets.For a general physical system, the presence of an extra invariant (in addition to the energy-momentum and wave action) is extremely rare. We summarize the unique conservation properties of geophysical fluid dynamics (with the beta effect) that allow for the existence of the extra invariant, and argue that its presence in various geophysical systems is a strong indication that the formation of zonal jets is indeed related to the extra invariant.Also, we develop a new, more direct, way to establish extra invariants (without using cubic corrections). For this, we introduce the small denominator lemma.

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“…Eventually the beam only retains the components with smaller k (larger wavelengths). Of course, additional factors must also be considered, such as geometric focusing effects (for non-planar waves) that may enhance the amplitude of the waves [8], in contrast to focusing onto wave attractors due to reflections off boundaries at oblique angles to the rotation axis [28]. The thickness of the wave beam δ(x) changes with the distance x travelled from the perturbation source via viscous spreading.…”

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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Turbulence and columnar vortex formation through inertial-wave focusing

Cited by 22 publications

References 14 publications

Excitation and resonant enhancement of axisymmetric internal wave modes

Excitation and resonant enhancement of axisymmetric internal wave modes

The Rossby wave extra invariant in the dynamics of 3-D fluid layers and the generation of zonal jets

Inertial waves in rapidly rotating flows: a dynamical systems perspective

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