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Decaying turbulence in a stratified fluid of high Prandtl number

Published online by Cambridge University Press:  12 July 2019

Shinya Okino Open the ORCID record for Shinya Okino [Opens in a new window]  and
Hideshi Hanazaki Open the ORCID record for Hideshi Hanazaki [Opens in a new window]
Shinya Okino*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan
Hideshi Hanazaki
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan
*
†Email address for correspondence: [email protected]
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Abstract

Decaying turbulence in a density-stratified fluid with a Prandtl number up to $Pr=70$ is investigated by direct numerical simulation. In turbulent flow with a Prandtl number larger than unity, it is well known that the passive scalar fluctuations cascade to scales smaller than the Kolmogorov scale, and show the $k^{-1}$ spectrum in the viscous–convective range, down to the Batchelor scale. In decaying stratified turbulence, the same phenomenon is initially observed for the buoyant scalar of high $Pr~(=70)$, until the Ozmidov scale becomes small and the buoyancy becomes effective even at the Kolmogorov scale. After that moment, however, the velocity components near the Kolmogorov scale begin to show strong anisotropy dominated by the vertically sheared horizontal flow, which reduces the vertical scale of density fluctuations. An analysis similar to that of Batchelor (J. Fluid Mech., vol. 5, 1959, pp. 113–133) indeed shows that the vertically sheared horizontal flow reduces the vertical scale of density fluctuations, without changing the horizontal scale.

JFM classification

Geophysical and Geological Flows: Internal waves Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 821 - 855
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Copyright
© 2019 Cambridge University Press 

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