Interaction between counterpropagating Rossby waves and capillary waves in planar shear flows

Biancofiore, Luca; Gallaire, François; Heifetz, Eyal

doi:10.1063/1.4916285

Cited by 18 publications

(24 citation statements)

References 23 publications

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“…The vorticity wave interaction approach has been applied this far to resonant instability between Rossby (Heifetz et al, 1999), gravity (Carpenter et al, 2011), capillary (Biancofiore et al, 2015), and even Alfven waves in shear dynamics of plasma . Hence, it is our aim to analyze the other resonant instability mechanisms obtained in swirling flow experiments with lower rotation rates, where both Rossby and inertial waves participate in the resonant instability mechanism.…”

Section: Discussionmentioning

confidence: 99%

Physical mechanism of centrifugal-gravity wave resonant instability in azimuthally symmetric swirling flows

2017

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We present an explicit analysis of wave-resonant instability of swirling flows inside fast rotating cylindrical containers. The linear dynamics are decomposed into the interaction between the horizontal inner centrifugal edge waves, the outer vertical gravity waves with the aim of understanding the dynamics of the centrifugal waves. We show how the far field velocity induced respectively by the centrifugal and the gravity waves affect each other's propagation rates and amplitude growth. We follow this with an analysis of the instability in terms of a four wave interaction, two centrifugal and two gravity ones, and explain why the resonant instability can be obtained only between a pair of two counter-propagating waves, one centrifugal and one gravity. Furthermore, a near resonant regime which does not yield instability is shown to result from a phase-locking configuration between a pair of a counter-propagating centrifugal wave and a pro-propagating gravity one, where the interaction affects the waves' propagation rates but not the amplitude growth.

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Section: Discussionmentioning

confidence: 99%

Physical mechanism of centrifugal-gravity wave resonant instability in azimuthally symmetric swirling flows

2017

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“…The vorticity wave interaction in stratified shear flows has been generalized further to include non-Boussinesq effects , as well as surface tension between immiscible fluids (Biancofiore et al 2015). It has been implemented for swirling flow instability in rotating cylinders (Yellin-Bergovoy et al 2017), and even for Alfvén waves in magneto-hydrodynamic shear flows .…”

Section: Discussionmentioning

confidence: 99%

A generalized action-angle representation of wave interaction in stratified shear flows

Heifetz

Guha

2017

J. Fluid Mech.

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In this paper we express the linearized dynamics of interacting interfacial waves in stratified shear flows in the compact form of action-angle Hamilton equations. The pseudo-energy serves as the Hamiltonian of the system, the action coordinates are the contribution of the interfacial waves to the wave-action, and the angles are their phases. The term "generalized action-angle" aims to emphasize that the action of each wave is generally time dependent and this allows instability. An attempt is made to relate this formalism to the action at a distance resonance instability mechanism between counterpropagating vorticity waves via the global conservations of pseudo-energy and pseudomomentum.

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“…There are even other ways of dynamic generation of vorticity, e.g. magnetic fields , surface tension (Biancofiore et al 2015), etc.…”

Section: The General Modelmentioning

confidence: 99%

Nonlinear dynamics induced by linear wave interactions in multilayered flows

Guha

Udwadia

2017

J. Fluid Mech.

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Using simple kinematics, we propose a general theory of linear wave interactions between the interfacial waves of a two dimensional (2D), inviscid, multi-layered fluid system. The strength of our formalism is that one does not have to specify the physics of the waves in advance. Wave interactions may lead to instabilities, which may or may not be of the familiar "normal-mode" type. Contrary to intuition, the underlying dynamical system describing linear wave interactions is found to be non-linear. Specifically, a saw-tooth jet profile with three interfaces possessing kinematic and geometric symmetry is explored. Fixed points of the system for different ranges of a Froude number like control parameter γ are derived, and their stability evaluated. Depending upon the initial condition and γ, the dynamical system may reveal transient growth, weakly positive Lyapunov exponents, as well as different non-linear phenomena such as formation of periodic and pseudoperiodic orbits. All these occur for those ranges of γ where normal-mode theory predicts neutral stability. Such rich non-linear phenomena is not observed in 2D dynamical system resulting from the 2-wave problem, which only reveals stable and unstable nodes.

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Interaction between counterpropagating Rossby waves and capillary waves in planar shear flows

Cited by 18 publications

References 23 publications

Physical mechanism of centrifugal-gravity wave resonant instability in azimuthally symmetric swirling flows

Physical mechanism of centrifugal-gravity wave resonant instability in azimuthally symmetric swirling flows

A generalized action-angle representation of wave interaction in stratified shear flows

Nonlinear dynamics induced by linear wave interactions in multilayered flows

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