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Parametrically forced stably stratified flow in a three-dimensional rectangular container

Published online by Cambridge University Press:  05 August 2020

Jason Yalim Open the ORCID record for Jason Yalim [Opens in a new window] ,
Juan M. Lopez Open the ORCID record for Juan M. Lopez [Opens in a new window]  and
Bruno D. Welfert Open the ORCID record for Bruno D. Welfert [Opens in a new window]
Jason Yalim
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ85287, USA
Juan M. Lopez*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ85287, USA
Bruno D. Welfert
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ85287, USA
*
†Email address for correspondence: [email protected]
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Abstract

The dynamics of a stably and thermally stratified fluid-filled cavity harmonically forced in the vertical direction, resulting in a periodic gravity modulation, is studied numerically. Prior simulations in a two-dimensional cavity showed a myriad of complex dynamic behaviours near the onset of instabilities, and here we address the extent to which these persist in three dimensions. Focusing on a parameter regime where the primary subharmonic mode is resonantly driven, we demonstrate comprehensive qualitative agreement between the dynamics in two and three dimensions; the quantitative difference is due to the larger forcing amplitudes needed in three dimensions to overcome the additional viscous damping from the spanwise walls. Using a small detuning of the forcing frequency, together with a relatively large forcing amplitude, leads to a wave-breaking regime where the qualitative agreement between two and three dimensions breaks down.

JFM classification

Geophysical and Geological Flows: Internal waves Instability: Parametric instability
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 900 , 10 October 2020 , R3
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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Yalim et al. supplementary movie 1

Animations over two forcing periods of the spanwise component of vorticity, the normalized Q-criterion, and isotherms for the four subharmonic limit cycles shown in figure 4.
Download Yalim et al. supplementary movie 1(Video)
Video 9.7 MB

Yalim et al. supplementary movie 2

Animation of the normalized Q-criterion for a quasiperiodic state in figure 5, strobed every two forcing periods.

Download Yalim et al. supplementary movie 2(Video)
Video 1.4 MB

Yalim et al. supplementary movie 3

Animation of the normalized Q-criterion for a quasiperiodic state in figure 6, strobed every two forcing periods.

Download Yalim et al. supplementary movie 3(Video)
Video 6.2 MB

Yalim et al. supplementary movie 4

Isotherms during a ten-forcing period transient wave-breaking event at forcing frequency 1.34 and forcing amplitude 0.3; see figure 7.

Download Yalim et al. supplementary movie 4(Video)
Video 29 MB

Yalim et al. supplementary movie 5

Normalized Q-criterion colored by temperature during a ten-forcing period transient wave-breaking event at forcing frequency 1.34 and forcing amplitude 0.3; see figure 7.

Download Yalim et al. supplementary movie 5(Video)
Video 45.1 MB

Yalim et al. supplementary movie 6

Isotherms and normalized Q-criterion during a ten-forcing period transient wave-breaking event at forcing frequency 1.34 and forcing amplitude 0.3; see figure 8.

Download Yalim et al. supplementary movie 6(Video)
Video 48.9 MB