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The energetics of mixing in continuous gravity currents

Published online by Cambridge University Press:  16 October 2025

Mohamad Harrouk Open the ORCID record for Mohamad Harrouk [Opens in a new window] ,
Rabah Mehaddi Open the ORCID record for Rabah Mehaddi [Opens in a new window] ,
Boris Arcen Open the ORCID record for Boris Arcen [Opens in a new window]  and
Yvan Dossmann
Mohamad Harrouk*
Affiliation:
Université de Lorraine, CNRS, LEMTA, Nancy F-54000, France
Rabah Mehaddi
Affiliation:
Université de Lorraine, CNRS, LEMTA, Nancy F-54000, France
Boris Arcen
Affiliation:
Université de Lorraine, CNRS, LEMTA, Nancy F-54000, France
Yvan Dossmann
Affiliation:
Université de Lorraine, CNRS, LEMTA, Nancy F-54000, France ENSL, CNRS, Laboratoire de Physique, Lyon F-69342, France
*
Corresponding author: Mohamad Harrouk, mohamad.harrouk@univ-lorraine.fr
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Abstract

We investigate the energetics of mixing induced by a continuously supplied dense current (density $\rho _0$) propagating beneath a lighter ambient fluid (density $\rho _a$) along a horizontal rigid boundary within a rectangular domain. The flow fields are computed using direct numerical simulations (DNS) performed with the Nek5000 spectral element solver. Mixing is quantified through the temporal evolution of the background potential energy, which exhibits a linear increase over time. This linear trend enables the definition of a dimensionless mixing parameter $\gamma$, representing the rate of background potential energy growth. The value of $\gamma$ depends on the initial density contrast for a fixed volumetric discharge at the source, characterised by the dimensionless source Froude number. The results reveal a non-monotonic dependence of $\gamma$ on the source Froude number, highlighting a complex interaction between flow forcing and mixing efficiency. We find that, under the assumption of uniform mixing along the current’s length, a fraction $\gamma /2$ of the total supplied energy is invested in mixing along a horizontal distance equal to the height of the inlet.

JFM classification

Geophysical and Geological Flows: Gravity currents Mixing: Turbulent mixing Turbulent Flows: Turbulence simulation

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Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 1021 , 25 October 2025 , R2
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© The Author(s), 2025. Published by Cambridge University Press

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