Three-dimensionality of the triadic resonance instability of a plane inertial wave

Mora, Daniel Odens; Monsalve, Eduardo; Brunet, Maxime; Dauxois, Thierry; Cortet, Pierre-Philippe

doi:10.1103/physrevfluids.6.074801

Cited by 12 publications

(12 citation statements)

References 61 publications

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“…We also note that adding rotation increases the wave instability and the 3-D effects, and is more likely to create symmetry breakings (such as, in our case, the creation of pure cylindrical modes with an azimuthal wavenumber out of an axisymmetric forcing wave field) (Maurer, Joubaud & Odier 2016; Ha, Chomaz & Ortiz 2021; Mora et al. 2021).…”

Section: Unconfined Domains: Triadic Resonant Instabilitymentioning

confidence: 87%

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Triadic resonant instability in confined and unconfined axisymmetric geometries

Boury

Maurer²,

Joubaud³

et al. 2023

J. Fluid Mech.

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We present an investigation of the resonance conditions governing triad interactions of cylindrical internal waves, i.e. Kelvin modes, described by Bessel functions. Our analytical study, supported by experimental measurements, is performed both in confined and unconfined axisymmetric domains. We are interested in two conceptual questions: can we find resonance conditions for a triad of Kelvin modes? What is the impact of the boundary conditions on such resonances? In both the confined and unconfined cases, we show that sub-harmonics can be spontaneously generated from a primary wave field if they satisfy at least a resonance condition on their frequencies of the form $\omega _0 = \pm \omega _1 \pm \omega _2$ . We demonstrate that the resulting triad is also spatially resonant, but that the resonance in the radial direction may not be exact in confined geometries due to the prevalence of boundary conditions – a key difference compared with Cartesian plane waves.

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Section: Unconfined Domains: Triadic Resonant Instabilitymentioning

confidence: 87%

“…Recent works have explored the implications of a three-dimensional (3-D) domain, still with plane wave forcings (see e.g. Mora et al 2021).…”

Section: Introductionmentioning

confidence: 99%

Triadic resonant instability in confined and unconfined axisymmetric geometries

Boury

Maurer²,

Joubaud³

et al. 2023

J. Fluid Mech.

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“…These promising experimental results are here to “feed” different theoretical approaches, as they complement the picture drawn by nuclear magnetic resonance on a librating superfluid 3 He ( 40 ). In particular, the initial threshold has to be linked to the Donnelly-Glaberson ( 41 ) instability, and the waves triggered on the lattice can be inertial ( 42 ) Kelvin or Tkachenko waves depending on the regime considered ( 43 , 44 ). A thorough comparison between these experimental results and theoretical approaches ( 45 ) could lead to a proper description of the particle/vortex interaction and a better understanding of the value of the coefficients in Schwarz’s equation ( 46 ).…”

Section: Discussionmentioning

confidence: 99%

Direct visualization of the quantum vortex lattice structure, oscillations, and destabilization in rotating ⁴ He

et al. 2023

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Quantum vortices are a core element of superfluid dynamics and elusively hold the keys to our understanding of energy dissipation in these systems. We show that we are able to visualize these vortices in the canonical and higher-symmetry case of a stationary rotating superfluid bucket. Using direct visualization, we quantitatively verify Feynman’s rule linking the resulting quantum vortex density to the imposed rotational speed. We make the most of this stable configuration by applying an alternative heat flux aligned with the axis of rotation. Moderate amplitudes led to the observation of collective wave mode propagating along the vortices, and high amplitudes led to quantum vortex interactions. When increasing the heat flux, this ensemble of regimes defines a path toward quantum turbulence in rotating 4 He and sets a baseline to consolidate the descriptions of all quantum fluids.

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“…In a more recent study, Mora et al. (2021) showed that the subharmonic waves produced by TRI do not propagate in the same vertical plane as the base inertial wave, thus establishing the three-dimensional (3-D) nature of TRI even at small primary wave amplitudes. Using classical triadic resonance equations for small primary wave amplitudes, Mora et al.…”

Section: Introductionmentioning

confidence: 99%

“…Using classical triadic resonance equations for small primary wave amplitudes, Mora et al. (2021) elucidated the 3-D nature of TRI in inertial waves. In this study, we perform a linear stability analysis of plane inertial waves using the local stability approach.…”

Section: Introductionmentioning

confidence: 99%

Short-wavelength instabilities in a finite-amplitude plane inertial wave

Abhiram,

Mathur

2024

J. Fluid Mech.

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We perform a linear stability analysis of a finite-amplitude plane inertial wave (of frequency $\omega$ in the range $0\le \omega \le f$ , where $f$ is the Coriolis frequency) by considering the inviscid evolution of three-dimensional (3-D), small-amplitude, short-wavelength perturbations. Characterizing the base flow plane inertial wave by its non-dimensional amplitude $A$ and the angle $\varPhi$ that its wavevector makes with the horizontal axis, the local stability equations are solved over the entire range of perturbation wavevector orientations. At sufficiently small $A$ , 3-D parametric subharmonic instability (PSI) is the only instability mechanism, with the most unstable perturbation wavevector making an angle close to $60^{\circ }$ with the inertial wave plane. In addition, the most unstable perturbation is shear-aligned with the inertial wave in the inertial wave plane. Further, at large $\varPhi$ , i.e. $\omega \approx f,$ there exists a wide range of perturbation wavevectors whose growth rate is comparable to the maximum growth rate. As $A$ is increased, theoretical PSI estimates become less relevant in describing the instability characteristics, and the dominant instability transitions to a two-dimensional (2-D) shear-aligned instability, which is shown to be driven by third-order resonance. The transition from 3-D PSI to a 2-D shear-aligned instability is shown to be reasonably captured by two different criteria, one based on the nonlinear time scale in the inertial wave and the other being a Rossby-number-based one.

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Three-dimensionality of the triadic resonance instability of a plane inertial wave

Cited by 12 publications

References 61 publications

Triadic resonant instability in confined and unconfined axisymmetric geometries

Triadic resonant instability in confined and unconfined axisymmetric geometries

Direct visualization of the quantum vortex lattice structure, oscillations, and destabilization in rotating ⁴ He

Short-wavelength instabilities in a finite-amplitude plane inertial wave

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Three-dimensionality of the triadic resonance instability of a plane inertial wave

Cited by 12 publications

References 61 publications

Triadic resonant instability in confined and unconfined axisymmetric geometries

Triadic resonant instability in confined and unconfined axisymmetric geometries

Direct visualization of the quantum vortex lattice structure, oscillations, and destabilization in rotating 4 He

Short-wavelength instabilities in a finite-amplitude plane inertial wave

Contact Info

Product

Resources

About

Direct visualization of the quantum vortex lattice structure, oscillations, and destabilization in rotating ⁴ He