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Dokl. Akad. Nauk, 2012, Volume 444, Number 2, Pages 156–159 (Mi dan24872)  

This article is cited in 4 scientific papers (total in 4 papers)

MECHANICS

Formation of wave on an ice-sheet above the dipole, moving in a fluid

A. T. Il'ichev, A. A. Savin, A. S. Savin

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow

Abstract: Theory of wave motions of a fluid with an ice-sheet was developed due to the necessity of solving of a number of problems of marine and land physics. The main attention in these investigations was focused on propagation and interaction of free waves, and also on appearance of waves under action of different loadings on the ice-sheet. From the other side, the problems dealing with waves on the fluid surface, free from the ice due to motion in the mass of the fluid of rigid bodies, has the known solutions. In this connection, it seems natural to disserminate the formulation and methods of such problems to the case of the fluid with the ice-sheet. In the present note we describe the character of formation of waves from the singularity, localized in the fluid of infinite depth beneath the ice-sheet. We use the example of the dipole, which models a cylinder in the infinite mass of the fluid. The character of the formation does not depend on the type of singularity. The ice-sheet is considered as a thin elastic plate of a constant width, floating on the water surface.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00335
The work is supported by the RFBR Grant No. 11-01-00335.



English version:
Doklady Mathematics, 2012, 57:5, 202–205

Bibliographic databases:

Document Type: Article
Received: 15.12.2011

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. T. Il'ichev, “Soliton-like structures on a water-ice interface”, Russian Math. Surveys, 70:6 (2015), 1051–1103  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. T. Il'ichev, V. Ya. Tomashpolskii, “Soliton-like structures on a liquid surface under an ice cover”, Theoret. and Math. Phys., 182:2 (2015), 231–245  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. S. Savin, N. E. Gorlova, P. A. Strunin, “Chislennoe modelirovanie vozdeistviya tochechnogo impulsnogo istochnika v zhidkosti na ledyanoi pokrov”, Mat. modelir. i chisl. metody, 2017, no. 13, 78–90  mathnet  crossref
    4. A. T. Il'ichev, A. S. Savin, “Process of establishing a plane-wave system on ice cover over a dipole moving uniformly in an ideal fluid column”, Theoret. and Math. Phys., 193:3 (2017), 1801–1810  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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