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A note on impulsive sphere motion beneath a free surface. (English) Zbl 1017.76012

Summary: We present a general framework for solving the impulsive oblique motion of a spherical body in close proximity and below a free surface. The fluid is considered to be impulsive, and the flow as incompressible. The irrotational flow field is deduced from velocity potential. The full nonlinear problem is reduced to a sequence of linear boundary value problems by employing a small-time expansion technique. The mixed boundary conditions are of Dirichlet type on the undisturbed free surface, and of Neumann type on the equilibrium spherical shape. The solution is obtained by employing Green’s function and the method of multipoles expansions. General expressions, correct in the small time, are given for free-surface deflections and for pressure force experienced by the moving sphere.

MSC:

76B07 Free-surface potential flows for incompressible inviscid fluids
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
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