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

Karima Khusnutdinova

doi:10.2205/2020ES000734

LONG INTERNAL RING WAVES IN A TWO-LAYER FLUID WITH AN UPPER-LAYER CURRENT Long internal ring waves in a two-layer fluid with an upper-layer current

АА Аа

Published in Russian Journal of Earth Sciences · Volume 20, Issue 4 · Rubric: ORIGINAL ARTICLES

DOI: https://doi.org/10.2205/2020ES000734

Received: 29.10.2021 Accepted: 26.07.2023 Language of publication: ENG

Authors

Karima Khusnutdinova

Loughborough University

ABSTRACT

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.

KEYWORDS

Stratified shear flows, internal waves, long-wave instability

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This work is licensed under Creative Commons Attribution 4.0 International Creative Commons

GOST

Khusnutdinova K. Long internal ring waves in a two-layer fluid with an upper-layer current // Russian Journal of Earth Sciences. 2020. no. 4. pp. -. DOI: https://doi.org/10.2205/2020ES000734. (Date of access 19.10.2026).

MLA

Karima Khusnutdinova. "Long internal ring waves in a two-layer fluid with an upper-layer current." Russian Journal of Earth Sciences 20.4 (2020): -. DOI: https://doi.org/10.2205/2020ES000734.

APA

Khusnutdinova K. (2020). Long internal ring waves in a two-layer fluid with an upper-layer current. Russian Journal of Earth Sciences, 20(4), -. https://doi.org/10.2205/2020ES000734

Chicago

Karima Khusnutdinova. "Long internal ring waves in a two-layer fluid with an upper-layer current." Russian Journal of Earth Sciences 20, no. 4 (2020): -. https://doi.org/10.2205/2020ES000734.

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{{cite journal | author = Khusnutdinova K. | title = Long internal ring waves in a two-layer fluid with an upper-layer current | journal = Russian Journal of Earth Sciences | year = 2020 | volume = 20 | issue = 4 | pages = - | doi = 10.2205/2020ES000734 }}

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LONG INTERNAL RING WAVES IN A TWO-LAYER FLUID WITH AN UPPER-LAYER CURRENT Long internal ring waves in a two-layer fluid with an upper-layer current

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