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Destratification of thermally stratified turbulent open-channel flow by surface cooling

Published online by Cambridge University Press:  28 July 2020

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: michael.kirkpatrick@sydney.edu.au
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Abstract

Destratification of thermally stratified open-channel flow by surface cooling is investigated using direct numerical simulation. The initial states are the equilibrium states resulting from radiative heating. Using these states as initial conditions, a series of direct numerical simulations was run with radiative heating removed and a constant, uniform cooling flux applied at the upper surface. The flow evolves until the initial stable stratification is broken down and replaced by unstable stratification driven by surface cooling. The destratification process is described with reference to the evolution of the internal structure of the turbulent flow field. Based on these observations, we conclude that the dominant time scales in the flow from the perspective of destratification are the time scales associated with shear ${t}_{\tau }$, convection ${t}_*$ and stable density stratification ${t}_N$. Scaling arguments are then used to derive a scaling relationship for destratification rate as a function of a friction Richardson number $Ri_{\tau } = ( {t}_{\tau }/ {t}_N)^2$ and a convection Richardson number $Ri_* = ( {t}_*/ {t}_N)^2$. The relationship takes the form ${\mathcal {D}}_N = C_1Ri_{\tau }^{-1} + C_2Ri_*^{-1}$, where ${\mathcal {D}}_N$ is the destratification rate non-dimensionalised with respect to $ {t}_N$ and $C_1$ and $C_2$ are model coefficients. The relationship is compared with simulation results and is shown to accurately predict the destratification rate in the simulations across a range of parameters. This relationship is then integrated to give a formula for the time taken for the flow to destratify.

JFM classification

Geophysical and Geological Flows: Stratified flows Turbulent Flows: Turbulent convection Geophysical and Geological Flows: River dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A29
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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Kirkpatrick et al. supplementary movie 2

Evolution of temperature and vorticity fields for time, t = 1 to 2. Top panel temperature. Bottom panel vorticity. Temperature range: -18 to 45. Vorticity range: 0 to 300.

Download Kirkpatrick et al. supplementary movie 2(Video)
Video 9.5 MB

Kirkpatrick et al. supplementary movie 3

Evolution of temperature and vorticity fields for time, t = 2 to 3. Top panel temperature. Bottom panel vorticity. Temperature range: -15 to 20. Vorticity range: 0 to 300.

Download Kirkpatrick et al. supplementary movie 3(Video)
Video 9.6 MB

Kirkpatrick et al. supplementary movie 4

Evolution of temperature and vorticity fields for time, t = 3 to 4. Top panel temperature. Bottom panel vorticity. Temperature range: -25 to 8. Vorticity range: 0 to 300.

Download Kirkpatrick et al. supplementary movie 4(Video)
Video 9.2 MB

Kirkpatrick et al. supplementary movie 5

Evolution of temperature and vorticity fields for time, t = 4 to 5. Top panel temperature. Bottom panel vorticity. Temperature range: -25 to 3. Vorticity range: 0 to 300.

Download Kirkpatrick et al. supplementary movie 5(Video)
Video 9.7 MB