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Evolution of thermally stratified turbulent open channel flow after removal of the heat source

Published online by Cambridge University Press:  01 August 2019

Michael P. Kirkpatrick Open the ORCID record for Michael P. Kirkpatrick [Opens in a new window] ,
N. Williamson Open the ORCID record for N. Williamson [Opens in a new window] ,
S. W. Armfield  and
V. Zecevic
Michael P. Kirkpatrick*
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW2006, Australia
N. Williamson
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW2006, Australia
S. W. Armfield
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW2006, Australia
V. Zecevic
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW2006, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Evolution of thermally stratified open channel flow after removal of a volumetric heat source is investigated using direct numerical simulation. The heat source models radiative heating from above and varies with height due to progressive absorption. After removal of the heat source the initial stable stratification breaks down and the channel approaches a fully mixed isothermal state. The initial state consists of three distinct regions: a near-wall region where stratification plays only a minor role, a central region where stratification has a significant effect on flow dynamics and a near-surface region where buoyancy effects dominate. We find that a state of local energetic equilibrium observed in the central region of the channel in the initial state persists until the late stages of the destratification process. In this region local turbulence parameters such as eddy diffusivity $k_{h}$ and flux Richardson number $R_{f}$ are found to be functions only of the Prandtl number $Pr$ and a mixed parameter ${\mathcal{Q}}$, which is equal to the ratio of the local buoyancy Reynolds number $Re_{b}$ and the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$. Close to the top and bottom boundaries turbulence is also affected by $Re_{\unicode[STIX]{x1D70F}}$ and vertical position $z$. In the initial heated equilibrium state the laminar surface layer is stabilised by the heat source, which acts as a potential energy sink. Removal of the heat source allows Kelvin–Helmholtz-like shear instabilities to form that lead to a rapid transition to turbulence and significantly enhance the mixing process. The destratifying flow is found to be governed by bulk parameters $Re_{\unicode[STIX]{x1D70F}}$, $Pr$ and the friction Richardson number $Ri_{\unicode[STIX]{x1D70F}}$. The overall destratification rate ${\mathcal{D}}$ is found to be a function of $Ri_{\unicode[STIX]{x1D70F}}$ and $Pr$.

JFM classification

Geophysical and Geological Flows: River dynamics Geophysical and Geological Flows: Stratified flows Mixing: Turbulent mixing
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 876 , 10 October 2019 , pp. 356 - 412
Copyright
© 2019 Cambridge University Press 

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