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On the scaling of shear-driven entrainment: a DNS study

Published online by Cambridge University Press:  30 August 2013

Harm J. J. Jonker ,
Maarten van Reeuwijk ,
Peter P. Sullivan  and
Edward G. Patton
Harm J. J. Jonker*
Affiliation:
Department Geoscience and Remote Sensing, Delft University, PO Box 5048, 2600 GA Delft, The Netherlands
Maarten van Reeuwijk
Affiliation:
Department of Civil and Environmental Engineering, Imperial College, London SW7 2AZ, UK
Peter P. Sullivan
Affiliation:
National Center for Atmospheric Research, Boulder, CO 80305, USA
Edward G. Patton
Affiliation:
National Center for Atmospheric Research, Boulder, CO 80305, USA
*
†Email address for correspondence: [email protected]
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Abstract

The deepening of a shear-driven turbulent layer penetrating into a stably stratified quiescent layer is studied using direct numerical simulation (DNS). The simulation design mimics the classical laboratory experiments by Kato & Phillips (J. Fluid Mech., vol. 37, 1969, pp. 643–655) in that it starts with linear stratification and applies a constant shear stress at the lower boundary, but avoids sidewall and rotation effects inherent in the original experiment. It is found that the layers universally deepen as a function of the square root of time, independent of the initial stratification and the Reynolds number of the simulations, provided that the Reynolds number is large enough. Consistent with this finding, the dimensionless entrainment velocity varies with the bulk Richardson number as $R{i}^{- 1/ 2} $. In addition, it is observed that all cases evolve in a self-similar fashion. A self-similarity analysis of the conservation equations shows that only a square root growth law is consistent with self-similar behaviour.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Turbulent Flows: Shear layer turbulence Turbulent Flows: Stratified turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 732 , 10 October 2013 , pp. 150 - 165
Copyright
©2013 Cambridge University Press 

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