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

Ron Yellin-Bergovoy1,*, Eyal Heifetz1, and Orkan M. Umurhan2

  • 1Department of Geophysics, School of Earth Sciences, Tel-Aviv University, Tel-Aviv, Israel
  • 2NASA Ames Research Center, Division of Space Sciences, Planetary Systems Branch, Moffett Field, California 94035, USA

  • *yellinr@post.tau.ac.il
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Phys. Rev. Fluids 2, 104801 – Published 11 October, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.104801

Abstract

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 and 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 counterpropagating 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 counterpropagating centrifugal wave and a propropagating gravity one, where the interaction affects the waves' propagation rates but not the amplitude growth.

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Phys. Rev. Fluids 2, 104801– Published 11 October, 2017
  • Received 6 February 2017

©2017 American Physical Society

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