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Prediction of frequencies in thermosolutal convection from mean flows

Sam E. Turton, Laurette S. Tuckerman, and Dwight Barkley
Phys. Rev. E 91, 043009 – Published 14 April 2015

Abstract

Motivated by studies of the cylinder wake, in which the vortex-shedding frequency can be obtained from the mean flow, we study thermosolutal convection driven by opposing thermal and solutal gradients. In the archetypal two-dimensional geometry with horizontally periodic and vertical no-slip boundary conditions, branches of traveling waves and standing waves are created simultaneously by a Hopf bifurcation. Consistent with similar analyses performed on the cylinder wake, we find that the traveling waves of thermosolutal convection have the RZIF property, meaning that linearization about the mean fields of the traveling waves yields an eigenvalue whose real part is almost zero and whose imaginary part corresponds very closely to the nonlinear frequency. In marked contrast, linearization about the mean field of the standing waves yields neither zero growth nor the nonlinear frequency. It is shown that this difference can be attributed to the fact that the temporal power spectrum for the traveling waves is peaked, while that of the standing waves is broad. We give a general demonstration that the frequency of any quasimonochromatic oscillation can be predicted from its temporal mean.

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  • Received 27 January 2015

DOI:https://doi.org/10.1103/PhysRevE.91.043009

©2015 American Physical Society

Authors & Affiliations

Sam E. Turton

  • DAMTP, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

Laurette S. Tuckerman

  • PMMH (UMR 7636 CNRS - ESPCI - UPMC Paris 6 - UPD Paris 7 - ParisTech - PSL) 10 rue Vauquelin, 75005 Paris, France

Dwight Barkley

  • Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

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Issue

Vol. 91, Iss. 4 — April 2015

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