Evanescent inertial waves

Nosan, Žiga; Burmann, Fabian; Davidson, P. A.; Noir, J.

doi:10.1017/jfm.2021.343

Cited by 3 publications

(3 citation statements)

References 7 publications

(9 reference statements)

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“…The scalings for are consistent with the findings from Nosan et al. (2021), where evanescent disturbances driven by forcing frequencies approximately equal to twice the mean rotation (i.e. ) were found to be ‘more or less independent of viscosity’ (i.e.…”

Section: Response To Low-amplitude Librationssupporting

confidence: 90%

“…These quantities, α K and α E , provide approximate power-law scalings of the form K ∼ E α K and Ē ∼ E α E within the given range of Ekman numbers, [E, 10E], confirming the observations made above in the limit E → 0: for 0 < ω 0.29, Ē ∼ E −1 , whereas for ω 1 K is independent of E and Ē ∼ E −0.5 . The scalings for ω 1 are consistent with the findings from Nosan et al (2021), where evanescent disturbances driven by forcing frequencies approximately equal to twice the mean rotation (i.e. ω ≈ 1) were found to be 'more or less independent of viscosity' (i.e.…”

Section: Global Responsessupporting

confidence: 87%

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Reflections and focusing of inertial waves in a tilted librating cube

Welfert

Lopez

2022

J. Fluid Mech.

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A fluid-filled cube rotating about an axis passing through the midpoints of opposite edges is subjected to small librations (i.e. modulation of the mean rotation). Low viscosity regimes, with Ekman number as small as $10^{-8}$ and equally small relative forcing amplitude, are explored numerically. The full inertial range of forcing frequencies, from 0 to twice the mean rotation rate are considered. The response flows are dominated by inertial wavebeams emitted from edges and/or vertices, depending on the forcing frequency. How these reflect on the cube's walls and focus onto edges and vertices lead to intricate patterns. Most of the results can be reconciled using linear inviscid ray-tracing theory with careful attention to wavebeam emissions and reflections. However, even at the low Ekman number and relative forcing amplitude considered, other effects are discernible which are not captured by ray tracing. These include a symmetry breaking due to viscous effects and a progressive wave, retrograde to the mean rotation and localized in the boundary layers of the cube, due to nonlinear effects and the librational forcing.

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Section: Response To Low-amplitude Librationssupporting

confidence: 90%

Section: Global Responsessupporting

confidence: 87%

Reflections and focusing of inertial waves in a tilted librating cube

Welfert

Lopez

2022

J. Fluid Mech.

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“…For inertial waves, Nosan et al [37] have shown theoretically and experimentally how, in a rotating fluid, waves of frequency slightly larger than the Coriolis parameter f may propagate horizontally over large distances, limited only by viscosity, despite being vertically evanescent. They mentioned the same phenomenon in a stratified fluid, where internal waves of frequency slightly larger than the buoyancy frequency N are evanescent horizontally but may propagate vertically over large distances, limited only by viscosity.…”

Section: Internal Gravity Wavesmentioning

confidence: 99%

Internal and inertia-gravity wave focusing at large Stokes numbers

et al. 2021

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Evanescent and inertial-like waves in rigidly rotating odd viscous liquids

Kirkinis,

Olvera de la Cruz

2024

J. Fluid Mech.

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Three-dimensional non-rotating odd viscous liquids give rise to Taylor columns and support axisymmetric inertial-like waves (J. Fluid Mech., vol. 973, 2023, A30). When an odd viscous liquid is subjected to rigid-body rotation however, there arise in addition a plethora of other phenomena that need to be clarified. In this paper, we show that three-dimensional incompressible or two-dimensional compressible odd viscous liquids, rotating rigidly with angular velocity $\varOmega$ , give rise to both oscillatory and evanescent inertial-like waves or a combination thereof (which we call of mixed type) that can be non-axisymmetric. By evanescent, we mean that along the radial direction, typically when moving away from a solid boundary, the velocity field decreases exponentially. These waves precess in a prograde or retrograde manner with respect to the rotating frame. The oscillatory and evanescent waves resemble respectively the body and wall-modes observed in (non-odd) rotating Rayleigh–Bénard convection (J. Fluid Mech., vol. 248, 1993, pp. 583–604). We show that the three types of waves (wall, body or mixed) can be classified with respect to pairs of planar wavenumbers $\kappa$ which are complex, real or a combination, respectively. Experimentally, by observing the precession rate of the patterns, it would be possible to determine the largely unknown values of the odd viscosity coefficients. This formulation recovers as special cases recent studies of equatorial or topological waves in two-dimensional odd viscous liquids which provided examples of the bulk–interface correspondence at frequencies $\omega <2\varOmega$ . We finally point out that the two- and three-dimensional problems are formally equivalent. Their difference then lies in the way data propagate along characteristic rays in three dimensions, which we demonstrate by classifying the resulting Poincaré–Cartan equations.

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Evanescent inertial waves

Abstract: Abstract

Cited by 3 publications

References 7 publications

Reflections and focusing of inertial waves in a tilted librating cube

Reflections and focusing of inertial waves in a tilted librating cube

Internal and inertia-gravity wave focusing at large Stokes numbers

Evanescent and inertial-like waves in rigidly rotating odd viscous liquids

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