Abstract
As is known, the study of impact in an ideal incompressible liquid in the classical formulation reduces to mixed problems of potential theory.
In the two-dimensional case their solution is facilitated by the use of the methods of complex variable function theory.
In the three-dimensional case the situation becomes more complex, particularly if the boundary of the volume occupied by the liquid has a complex shape. Therefore the influence of the bottom and walls of vessels on the distribution of the pressures and velocities during impact in the three-dimensional case has had little study.
In the present study we consider the vertical impact of a spherical body of diameter 2a which is half submerged in a liquid layer of finite depth (Fig. 1). Primary attention is devoted to the study of the influence of the bottom on the phenomena which take place during impact.
In the case when the bottom is spherical the question has been studied by Zhukovskii [1].
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References
N. E. Zhukovskii, “On the impact of two spheres, one of which floats in a liquid”, Collected Works [in Russian], 2, Gosizdat, 1949.
S. A. Belousov, Tables of Normed Adjoint Legendre Polynomials [in Russian], Izd-vo AN SSSR, 1956.
Reference Mathematical Library, Mathematical Analysis [in Russian], Fizmatgiz, 1961,
N. N. Lebedev, Special Functions and Their Applications [in Russian], Gostekhizdat, 1953.
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Vorovich, L.S. Vertical impact of a sphere half submerged in a liquid of finite depth. Fluid Dyn 1, 70–77 (1966). https://doi.org/10.1007/BF01020468
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DOI: https://doi.org/10.1007/BF01020468