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Long internal ring waves in a two-layer fluid with an upper-layer current
journal contribution
posted on 2020-06-23, 10:11 authored by Karima KhusnutdinovaKarima KhusnutdinovaWe 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 SciencesVolume
20Publisher
Geophysical Centre RASVersion
- AM (Accepted Manuscript)
Rights holder
© Geophysical Center RASPublisher 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
2020-06-14Publication date
2020-07-12Notes
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 birthdayISSN
1681-1208Publisher version
Language
- en
Depositor
Dr Karima Khusnutdinova. Deposit date: 21 June 2020Article number
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