Waves generated on an ice cover by a source pulsating in fluid. (English. Russian original) Zbl 1272.76062

Fluid Dyn. 48, No. 3, 303-309 (2013); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2013, No. 3, 24-30 (2013).
Summary: A point source of variable intensity located at rest in a plane infinitely deep fluid layer under an ice cover is considered. The general expression for perturbations of the fluid-ice interface is obtained. In the case of the long operation in the pulsating regime the wave established on the ice cover is found.


76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
86A40 Glaciology
86A05 Hydrology, hydrography, oceanography
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[1] A.T. Il’ichev, Solitary Waves in Hydrodynamics Models (Fizmatlit, Moscow, 2003) [in Russian].
[2] H. Lamb, Hydrodynamics (Cambridge Univ. Press, Cambridge, 1932; Gostekhizdat, Moscow, Leningrad, 1947).
[3] N.E. Kochin, I.A. Kibel’, and N.V. Roze, Theoretical Hydrodynamics, Vol. 1 (Gostekhizdat, Leningrad, Moscow, 1948) [in Russian].
[4] N.E. Kochin, ”Wave Drag and Lift of Submerged Bodies,” in: N.E. Kochin, Collected Works, Vol. 2 (USSR Academy of Sciences, Moscow, Leningrad, 1949) [in Russian], pp. 105–182.
[5] M.V. Keldysh and M.A. Lavrent’ev, ”Wing Motion above the Surface of a Heavy Fluid,” in: M.V. Keldysh, Selected Works. Mechanics (Nauka, Moscow, 1985) [in Russian], pp. 120–151.
[6] M.V. Keldysh, ”Notes on Certain Motions of Heavy Fluids,” in: M.V. Keldysh, Selected Works. Mechanics (Nauka, Moscow, 1985) [in Russian], pp. 100–103.
[7] L.N. Sretenskii, Theory of Wave Motions of Fluids (Nauka, Moscow, 1977) [in Russian].
[8] L.M. Milne-Thomson, Theoretical Hydrodynamics (Macmillian, New York, 1950; Mir, Moscow, 1964). · Zbl 0164.55802
[9] R.G. Chowdhury and B.N. Mandal, ”Motion due to Fundamental Singularities in Finite DepthWater with an Elastic Solid Cover,” Fluid Dynam. Res. 38, No. 4, 224–240 (2006). · Zbl 1135.76012
[10] D.Q. Lu and S.Q. Dai, ”Generation of Transient Waves by Impulsive Disturbances in an Inviscid Fluid with an Ice-Cover,” Arch. Appl. Mech. 76, No. 1–2, 49–63 (2006). · Zbl 1161.76441
[11] D.Q. Lu and S.Q. Dai, ”Flexural- and Capillary-Gravity Waves due to Fundamental Singularities in an Inviscid Fluid of Finite Depth,” Int. J. Eng. Sci. 46, No. 11, 1183–1193 (2008). · Zbl 1213.76069
[12] A.A. Savin and A.S. Savin, ”Ice Cover Perturbations by a Dipole in Motion within a Liquid,” Fluid Dynamics 47, No. 2, 139–146 (2012). · Zbl 1242.76021
[13] A.T. Il’ichev, A.A. Savin, and A.S. Savin, ”Establishment of a Wave on an Ice Cover above a Dipole Traveling in Fluid,” Dokl. Ros. Akad. Nauk 444, No. 2, 156–159 (2012).
[14] A.S. Savin, ”Establishment of Surface Waves Generated by Hydrodynamic Singularities in Plane Flow,” Fluid Dynamics 37, No. 3, 421–424 (2002). · Zbl 1161.76402
[15] A.T. Il’ichev and A.S. Savin, ”On the Process of Establishment of SurfaceWaves in Plane Flow,” Fluid Dynamics 39, No. 4, 574–581 (2004). · Zbl 1184.76627
[16] V.S. Vladimirov, Distributions in Mathematical Physics (Nauka, Moscow, 1976) [in Russian]. · Zbl 0524.46023
[17] W. Kecs and P. Teodoresku, Introducere in Teoria Distributitor cu Applicatii in Tehnica (Editure Tehnica, Bucharest, 1975; Mir, Moscow, 1978).
[18] M.A. Lavrent’ev and B.V. Shabat,Methods of Theory of Functions of a Complex Variable (Nauka, Moscow, 1987) [in Russian].
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