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Asymmetries in gravity currents attributed to the nonlinear equation of state

Published online by Cambridge University Press:  09 March 2021

Andrew P. Grace Open the ORCID record for Andrew P. Grace [Opens in a new window] ,
Marek Stastna Open the ORCID record for Marek Stastna [Opens in a new window] ,
Kevin G. Lamb Open the ORCID record for Kevin G. Lamb [Opens in a new window]  and
K. Andrea Scott Open the ORCID record for K. Andrea Scott [Opens in a new window]
Andrew P. Grace*
Affiliation:
Department of Applied Mathematics, University of Waterloo, WaterlooON N2L 3G1, Canada
Marek Stastna
Affiliation:
Department of Applied Mathematics, University of Waterloo, WaterlooON N2L 3G1, Canada
Kevin G. Lamb
Affiliation:
Department of Applied Mathematics, University of Waterloo, WaterlooON N2L 3G1, Canada
K. Andrea Scott
Affiliation:
Department of Systems Design Engineering, University of Waterloo, WaterlooON N2L 3G1, Canada
*
†Email address for correspondence: andrew.grace@uwaterloo.ca
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Abstract

For temperatures near the temperature of maximum density, 3.98 $^{\circ }$C for freshwater, the nonlinearity of the equation of state plays an important role in the density driven dynamics. In this study, we demonstrate that the nonlinear equation of state can lead to large scale differences in the spatial and temporal evolution of freshwater gravity currents when intruding and ambient temperatures are below the temperature of maximum density. The results of this study show that when the temperature of the intruding fluid decreases throughout the evolution of the gravity current, the density difference between the intrusion and the ambient decreases rapidly. When the temperature of intruding fluid increases throughout the evolution of the gravity current, the density difference decreases at a slower rate. The differing rates at which the density difference decreases lead to asymmetries in head location, and vertical extent of intruding fluid, and may have implications for larger scale flows in this temperature regime. These results are robust across the Grashof numbers studied.

JFM classification

Geophysical and Geological Flows: Gravity currents
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A18
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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