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Kinetic energy cascade in stably stratified open-channel flows

Published online by Cambridge University Press:  26 August 2021

Amir Atoufi Open the ORCID record for Amir Atoufi [Opens in a new window] ,
K. Andrea Scott  and
Michael L. Waite
Amir Atoufi*
Affiliation:
Department of Systems Design Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada
K. Andrea Scott
Affiliation:
Department of Systems Design Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Michael L. Waite
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, the kinetic energy cascade in stably stratified open-channel flows is investigated. A mathematical framework to incorporate vertical scales into the conventional kinetic energy spectrum and its budget is introduced. This framework defines kinetic energy density in horizontal spectral and vertical scale space. The energy cascade is studied by analysing the evolution of kinetic energy density. It is shown that energetic streamwise scales ($\lambda _x$) become larger with increasing vertical scale. For the strongest stratification, for which the turbulence becomes intermittent, the energetic streamwise scales are suppressed, and energy density resides in $\lambda _x$ of the size of the domain. It is shown that, in an unstratified case, vertical scales of the size comparable to the height of the logarithmic layer connect viscous regions to the outer layer. By contrast, in stratified cases, such a connection is not observed. Moreover, it is shown that nonlinear transfer for streamwise scales is dominated by in-plane triad interactions and inter-plane transfer is more active in transferring energy density among small vertical scales of the size comparable to the height of viscous sublayer. The vertical scales of size comparable to the height of the viscous sublayer and buffer layer are the most active scales in the viscous term and the production term in the energy density budget, respectively.

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulent boundary layers Geophysical and Geological Flows: Atmospheric flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 925 , 25 October 2021 , A25
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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