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Complex dynamics in a stratified lid-driven square cavity flow

Published online by Cambridge University Press:  20 September 2018

Ke Wu ,
Bruno D. Welfert  and
Juan M. Lopez Open the ORCID record for Juan M. Lopez [Opens in a new window]
Ke Wu
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
Bruno D. Welfert
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
Juan M. Lopez*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
*
†Email address for correspondence: [email protected]
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Abstract

The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier–Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.

JFM classification

Geophysical and Geological Flows: Internal waves Nonlinear Dynamical Systems: Nonlinear Dynamical Systems Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 43 - 66
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Copyright
© 2018 Cambridge University Press 

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Wu Supplementary Movie 1

Animations over one period of the deviations of the streamfunction from its mean for the limit cycle L5, L3 and L2 at Re and Ri as indicated.

Download Wu Supplementary Movie 1(Video)
Video 2.7 MB

Wu Supplementary Movie 2

Animations over one period of the deviations of the horizontal temperature from its means for the limit cycles L1 and L2 at Re and Ri as indicated.

Download Wu Supplementary Movie 2(Video)
Video 5.4 MB

Wu Supplementary Movie 3

Animations over 0.01 viscous time of the horizontal temperature of non-periodic states at Re=5000 and Ri as indicated.

Download Wu Supplementary Movie 3(Video)
Video 25.2 MB