Abstract
The two-dimensional unsteady problem of the development of wave motion in a two-layer finite-depth fluid bounded from above by a free surface is solved. The cases in which one of the layers is at rest in the unperturbed state and in other layer (near-surface or near-bottom) the horizontal flow velocity varies linearly with depth are considered. The dispersion relations and the group velocities of three wave modes arising in the presence of shear flow are determined. The vertical displacements of the free surface caused by switching-on of a pulsating source located in the initially immobile fluid layer are calculated. The problem is considered in a linear formulation, the fluid is assumed to be ideal and incompressible.
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REFERENCES
Wehausen, J.V. and Laitone, E.V., Surface waves, in: Handbuch der Physik, 1960, vol. 9, pp. 446–778.
Sretensky, L.N., Teoriya volnovykh dvizhenii zhidkosti (The Theory of Wave Motions of a Fluid), Moscow: Nauka, 1977.
Cherkesov, L.V., Gidrodinamika voln (Wave Hydrodynamics), Kiev, Naukova Dumka, 1980.
Peregrine, D.H., Interaction of water waves and currents, Adv. Appl. Mech., 1976, vol. 16, pp. 9–117.
Jonsson, I.G., Wave-current interactions, The Sea, 1990, vol. 9, pp. 65–120.
Bukatov, A.E., Vlasenko, V.I., Pukhtyar, L.D., Suvorov, A.M., et al., Dinamika poverkhnostnykh i vnutrennikh voln (Dynamics of Surface and Internal Waves), Kiev: Naukova Dumka, 1988.
Taylor, G., The action of a surface current used as a breakwater, Proc. Royal Soc. Lond. A., 1955, vol. 231, pp. 466–478.
Brevik, I., The stopping of linear gravity waves in currents of uniform vorticity, Phys. Norv., 1976, vol. 8, no. 3, pp. 157–162.
Brevik, I. and Sollie, R., Stable and unstable modes in a wave-current system having uniform vorticity, Phys. Scr., 1997, vol. 55, pp. 639–643.
Pavelyeva, E.B. and Savin, A.S., Establishment of waves generated by a pulsating source in a finite-depth fluid, Fluid Dyn., 2018, vol. 53, pp. 461–470.
Il’ichev, A.T. and Savin, A.S., Evolution of perturbations of a free surface from a pulsating underwater source in a fluid of finite depth, Fluid Dyn., 2021, vol. 56, no. 6, pp. 780–785. https://doi.org/10.1134/S0015462821060045
Sturova, I.V., The Cauchy–Poisson problem for fluid with an ice cover in the presence of shear current (two-dimensional case), Fluid Dyn., 2022, vol. 57, no. 1, pp. 45–54. https://doi.org/10.1134/S0015462822010104
Korn, G. and Korn, T., Mathematical Handbook for Scientists and Engineers, New York: McGraw-Hill, 1961; Moscow: Nauka, 1968.
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Translated by E.A. Pushkar
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Sturova, I.V. Action of a Pulsating Source in a Fluid in the Presence of a Shear Layer. Fluid Dyn 58, 520–531 (2023). https://doi.org/10.1134/S0015462823700088
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DOI: https://doi.org/10.1134/S0015462823700088