Variational mode decomposition for estimating critical reflected internal wave in stratified fluid

Horne, Edward P. W.; Schmitt, Jérémy; Pustelnik, Nelly; Joubaud, Sylvain; Odier, Philippe

doi:10.1007/s00348-021-03206-7

Cited by 2 publications

(1 citation statement)

References 46 publications

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“…While the effects of a critical slope in stratified systems have attracted extensive attention (e.g. Gordon 1980;Thorpe 1997;Slinn & Riley 1998;Dauxois & Young 1999;Javam, Imberger & Armfield 1999;Scotti 2011;Horne et al 2021), the situation in rotating systems has not been as systematically studied. This is in part due to internal waves lending themselves to being studied in planar two-dimensional systems, whereas inertial waves in rotating systems are intrinsically helical, with velocity and vorticity vectors parallel and in phase (Davidson 2013), and as such cannot be described in a planar two-dimensional setting (in which velocity and vorticity are orthogonal).…”

Section: Introductionmentioning

confidence: 99%

Boundary-confined waves in a librating cube

et al. 2022

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When a fluid-filled cube rotating rapidly about an axis passing through two opposite vertices is subjected to harmonic modulations of its rotation rate (librations) at a modulation frequency that is $2/\sqrt {3}$ times the mean rotation frequency, all walls of the cube have critical reflection slopes. As such, all inertial wave beams emitted from edges and vertices of the cube in response to the librations are trapped in thin oscillatory boundary layers for forcing amplitudes (Rossby numbers) below a critical value which depends on the Ekman number (ratio of rotation to viscous time scales). How the resulting oscillatory boundary layer flow, referred to as a boundary-confined wave, depends on Ekman and Rossby numbers is examined in detail over several decades. Of particular interest is how the mean flow grows with increasing forcing amplitude, leading to instability resulting from nonlinear interactions between the mean flow and waves in the oscillatory boundary layers, injecting intense small-scale structures throughout the cube.

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Section: Introductionmentioning

confidence: 99%

Boundary-confined waves in a librating cube

et al. 2022

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Instabilities in internal gravity waves

Varma¹,

Mathur²,

Dauxois

2022

MINE

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<abstract><p>Internal gravity waves are propagating disturbances in stably stratified fluids, and can transport momentum and energy over large spatial extents. From a fundamental viewpoint, internal waves are interesting due to the nature of their dispersion relation, and their linear dynamics are reasonably well-understood. From an oceanographic viewpoint, a qualitative and quantitative understanding of significant internal wave generation in the ocean is emerging, while their dissipation mechanisms are being debated. This paper reviews the current knowledge on instabilities in internal gravity waves, primarily focusing on the growth of small-amplitude disturbances. Historically, wave-wave interactions based on weakly nonlinear expansions have driven progress in this field, to investigate spontaneous energy transfer to various temporal and spatial scales. Recent advances in numerical/experimental modeling and field observations have further revealed noticeable differences between various internal wave spatial forms in terms of their instability characteristics; this in turn has motivated theoretical calculations on appropriately chosen internal wave fields in various settings. After a brief introduction, we present a pedagogical discussion on linear internal waves and their different two-dimensional spatial forms. The general ideas concerning triadic resonance in internal waves are then introduced, before proceeding towards instability characteristics of plane waves, wave beams and modes. Results from various theoretical, experimental and numerical studies are summarized to provide an overall picture of the gaps in our understanding. An ocean perspective is then given, both in terms of the relevant outstanding questions and the various additional factors at play. While the applications in this review are focused on the ocean, several ideas are relevant to atmospheric and astrophysical systems too.</p></abstract>

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Variational mode decomposition for estimating critical reflected internal wave in stratified fluid

Cited by 2 publications

References 46 publications

Boundary-confined waves in a librating cube

Boundary-confined waves in a librating cube

Instabilities in internal gravity waves

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