Simple solutions to the wave problem on the surface of a fluid with the linear hydroelastic model

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Abstract


The problem of generation of waves on the surface of a water layer placed on an elastic base is considered. It is assumed that the generating source is located inside the elastic half-space. The Podyapolskii approach is used which is based on study of the solutions to the common linear system of equations of the theory of elasticity in the half-space and the theory of water waves linked at the interface by the corresponding boundary conditions. The previously obtained simplified dispersion relation for the water mode with account for the elastic base effect is used to derive a simple integral formula which associates the initial perturbation of a special kind in the elastic half-space and the amplitude of the surface water waves generated by this source. The obtained solutions are compared with the solutions based on the well-known piston model of long wave generation.


About the authors

S. Yu. Dobrokhotov

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences; Moscow Institute of Physics and Technology

Email: ilyasov@ipmnet.ru

Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526; 9, Institutskij, Dolgoprudny, Moscow region, 141701

Kh. Kh. Il’yasov

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Author for correspondence.
Email: ilyasov@ipmnet.ru

Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526

S. Ya. Sekerzh-Zen’kovich

Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences

Email: ilyasov@ipmnet.ru

Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526

O. L. Tolstova

Moscow Institute of Physics and Technology; Steklov Mathematical Institute of Russian Academy of Sciences

Email: olga111@rambler.ru

Russian Federation, 9, Institutskij, Dolgoprudny, Moscow region, 141701; 8, Gubkina street, Moscow, 117966

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