Journal of Nonlinear Mathematical Physics

Volume 19, Issue 1, March 2012, Pages 98 - 118

Steady Internal Water Waves with a Critical Layer Bounded by the Wave Surface

Authors
Anca-Voichita Matioc
Institute for Applied Mathematics, Leibniz University of Hanover, Welfengarten 1, 30655 Hanover, Germany, matioca@ifam.uni-hannover.de
Received 20 August 2011, Accepted 28 November 2011, Available Online 6 January 2021.
DOI
https://doi.org/10.1142/S1402925112500088How to use a DOI?
Keywords
Internal waves, streamlines, vorticity, real-analytic
Abstract

In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the gradient of the stream function associated to the fluid beneath the interface vanishes, on the wave surface, at exactly two points. Furthermore, there exists a critical layer which is bounded from above by the wave profile. Besides, we prove, without excluding the presence of stagnation points, that if the vorticity function associated to each fluid in part is real-analytic, bounded, and non-increasing, then capillary-gravity steady internal waves are a priori real-analytic. Our new method provides the real-analyticity of capillary and capillary-gravity waves with stagnation points traveling over a homogeneous rotational fluid under the same restrictions on the vorticity function.

Copyright
© 2012 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
19 - 1
Pages
98 - 118
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925112500088How to use a DOI?
Copyright
© 2012 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Anca-Voichita Matioc
PY  - 2021
DA  - 2021/01
TI  - Steady Internal Water Waves with a Critical Layer Bounded by the Wave Surface
JO  - Journal of Nonlinear Mathematical Physics
SP  - 98
EP  - 118
VL  - 19
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925112500088
DO  - https://doi.org/10.1142/S1402925112500088
ID  - Matioc2021
ER  -