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Viscous gravity currents over flat inclined surfaces

Published online by Cambridge University Press:  23 November 2021

Herbert E. Huppert Open the ORCID record for Herbert E. Huppert [Opens in a new window] ,
Vitaly A. Kuzkin Open the ORCID record for Vitaly A. Kuzkin [Opens in a new window]  and
Svetlana O. Kraeva Open the ORCID record for Svetlana O. Kraeva [Opens in a new window]
Herbert E. Huppert
Affiliation:
Institute of Theoretical Geophysics, King's College, Cambridge CB2 1ST, UK
Vitaly A. Kuzkin
Affiliation:
Department of Theoretical Mechanics, Peter the Great St Petersburg Polytechnic University, St Petersburg 195251, Russia Laboratory for Discrete Models in Mechanics, Institute for Problems in Mechanical Engineering RAS, St Petersburg 199178, Russia
Svetlana O. Kraeva*
Affiliation:
Department of Theoretical Mechanics, Peter the Great St Petersburg Polytechnic University, St Petersburg 195251, Russia
*
†Email address for correspondence: [email protected]
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Abstract

Previous analyses of the flow of low-Reynolds-number, viscous gravity currents down inclined planes are investigated further and extended. Particular emphasis is on the motion of the fluid front and tail, which previous analyses treated somewhat cavalierly. We obtain reliable, approximate, analytic solutions in these regions, the accuracies of which are satisfactorily tested against our numerical evaluations. The solutions show that the flow has several time scales determined by the inclination angle, $\alpha$. At short times, the influence of initial and boundary conditions is important and the flow is governed by both the pressure gradient and the direct action of gravity due to inclination. Later on, the areas where the boundary conditions are important shrink. This fact explains why previous solutions, being inaccurate near the front and the tail, described experimental data with high accuracy. At larger times, of the order of $\alpha ^{-5/2}$, the influence of the pressure gradient may be neglected and the fluid profile converges to the square-root shape predicted in previous works. Important extensions of our approach are also outlined.

JFM classification

Geophysical and Geological Flows: Gravity currents Mathematical Foundations: General fluid mechanics Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , A12
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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