Abstract
A nonlinear problem of motion of a solid sphere near a free surface of an infinitely deep fluid is considered. For the case of motion with a constant acceleration starting from rest, the solution is studied using a small‐time expansion. Expansion coefficients up to the fourth power inclusive are found for the free surface elevation and for the force acting on the sphere. The solutions for linear and nonlinear conditions on the free surface are compared.
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REFERENCES
H. Lamb, “On some cases of wave motion on deep water,” Ann. Matematica, 21, 237-250 (1913).
T. H. Havelock, “The wave pattern of a doublet in a stream,” Proc. Roy. Soc. London, Ser. A, 121, 515-523 (1928).
G. X. Wu and E. Taylor, “Radiation and diffraction by submerged sphere at a forward speed,” Proc. Roy. Soc. London, Ser. A, 417, 433-461 (1995).
P. Tyvand and T. Miloh, “Free-surface ow due to impulsive motion of a submerged cylinder,” J. Fluid Mech., 286, 67-101 (1995).
P. Tyvand and T. Miloh, “Free-surface ow generated by a small submerged circular cylinder starting from rest,” ibid., pp. 103-116.
I. M. Mindlin, Integrodifferential Equations in Dynamics of a Heavy Stratified Fluid [in Russian], Nauka, Fizmatlit, Moscow (1996).
L. V. Ovsyannikov, N. I. Makarenko, V. I. Nalimov, et al., Nonlinear Problems of the Theory of Surface and Internal Waves [in Russian], Nauka, Novosibirsk (1985).
N. I. Makarenko, “Generation of nonlinear waves by a submerged cylinder,” in: Dynamics of Continuous Media (collected scientific papers) [in Russian], No. 113, Novosibirsk (1998), pp. 99-102.
E. V. Pyatkina, “Problem of generation of nonlinear waves by a submerged sphere,” in: Dynamics of Continuous Media (collected scientific papers) [in Russian], No. 118, Novosibirsk (2001), pp. 130-134.
E. V. Pyatkina, “Dipole approximation in the problem of generation of nonlinear waves by a submerged sphere,” in: Dynamics of Continuous Media (collected scientific papers) [in Russian], No. 116, Novosibirsk (2000), pp. 148-153.
N. S. Koshlyakov, Basic Differential Equations of Mathematical Physics [in Russian], ONTI, Moscow-Leningrad (1936).
E. V. Pyatkina, “Integral equation for normal velocity in the problem of wave generation by a submerged sphere,” in: Mathematical Models and Method of Their Investigation, Proc. Int. Conf. (Krasnoyarsk, August 16-21, 2001), Vol. 2, Inst. Numerical Simulation, Sib. Div., Russian Acad. of Sci., Krasnoyarsk (2001), pp. 157-161.
I. I. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York (1980).
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Pyatkina, E.V. Small‐Time Expansion of Wave Motion Generated by a Submerged Sphere. Journal of Applied Mechanics and Technical Physics 44, 32–43 (2003). https://doi.org/10.1023/A:1021721528143
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DOI: https://doi.org/10.1023/A:1021721528143