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Long internal ring waves in a two-layer fluid with an upper-layer current

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journal contribution
posted on 23.06.2020, 10:11 by Karima Khusnutdinova
We consider a two-layer fluid with a depth-dependent upper-layer current (e.g. a river inflow, an exchange flow in a strait, or a wind-generated current). In the rigid-lid approximation, we find the necessary singular solution of the nonlinear first-order ordinary differential equation responsible for the adjustment of the speed of the long interfacial ring wave in different directions in terms of the hypergeometric function. This allows us to obtain an analytical description of the wavefronts and vertical structure of the ring waves for a large family of the current profiles and to illustrate their dependence on the density jump and the type and the strength of the current. In the limiting case of a constant upper-layer current we obtain a 2D ring waves' analogue of the long-wave instability criterion for plane interfacial waves. On physical level, the presence of instability for a sufficiently strong current manifests itself already in the stable regime in the squeezing of the wavefront of the interfacial ring wave in the direction of the current. We show that similar phenomenon can also take place for other, depth-dependent currents in the family.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Russian Journal of Earth Sciences

Volume

20

Publisher

Geophysical Centre RAS

Version

AM (Accepted Manuscript)

Rights holder

© Geophysical Center RAS

Publisher statement

This is the peer reviewed version of the following article: Khusnutdinova Karima (2020), Long internal ring waves in a two-layer fluid with an upper-layer current, Russ. J. Earth Sci., 20, ES4006, doi:10.2205/2020ES000734, which has been published in final form at http://rjes.wdcb.ru/doi/2020ES000734-res.html.

Acceptance date

14/06/2020

Publication date

2020-07-12

Notes

17 pages, 10 figures, submitted to the Special Issue of the "Russian Journal of Earth Sciences" dedicated to Professor Efim Pelinovsky on the occasion of his 75th birthday

ISSN

1681-1208

Language

en

Depositor

Dr Karima Khusnutdinova. Deposit date: 21 June 2020

Article number

ES4006

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