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Steady circular hydraulic jump on a rotating disk

Published online by Cambridge University Press:  28 September 2021

Anna Ipatova Open the ORCID record for Anna Ipatova [Opens in a new window] ,
K.V. Smirnov Open the ORCID record for K.V. Smirnov [Opens in a new window]  and
E.I. Mogilevskiy Open the ORCID record for E.I. Mogilevskiy [Opens in a new window]
Anna Ipatova
Affiliation:
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie gory, 1, 119991 Moscow, Russia Université de Lille, CNRS, IEMN UMR 8520, F-59000 Lille, France
K.V. Smirnov
Affiliation:
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie gory, 1, 119991 Moscow, Russia
E.I. Mogilevskiy*
Affiliation:
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Leninskie gory, 1, 119991 Moscow, Russia
*
†Email address for correspondence: [email protected]
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Abstract

The paper deals with the steady axially symmetric flow of a viscous liquid layer over a rotating disk. The liquid is fed near the axis of rotation and spreads due to inertia and the centrifugal force. The viscous shallow-water approach gives a system of ordinary differential equations governing the flow. We consider inertia, gravity, centrifugal and Coriolis forces and estimate the effect of surface tension. We found four qualitatively different flow regimes. Transition through these regimes shows the continuous evolution of the flow structure from a hydraulic jump on a static disk to a monotonic thickness decrease on a fast rotating one. We show that, in the absence of surface tension, the intensity of the jump gradually vanishes at a finite distance from the axis of rotation while the angular velocity increases. The surface tension decreases the jump radius and destroys the steady solution for a certain range of parameters.

JFM classification

Interfacial Flows (free surface): Thin films Waves/Free-surface Flows: Hydraulics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 927 , 25 November 2021 , A24
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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