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Planing of a long plate. (English) Zbl 1367.74034

Summary: Previously we studied the two-dimensional problem of planing of a flat plate on the free surface of an incompressible inviscid fluid of infinite depth. We assumed that the Froude number \(U/(gL)^{1/2}\) was large, with \(U\) the horizontal velocity of the plate, \(L\) the length of the plate, and \(g\) the acceleration of gravity. We solved this problem by the method of matched asymptotic expansions, with \(gLU^{-2}\) as the small parameter. The solution contained a jet flowing up along the forward-facing surface of the plate. When the jet reached the upper edge of the plate, it became a free jet that followed a parabolic path and fell back onto the free surface. Now we consider the case where the jet falls off the plate before it reaches the upper edge, and we determine where it leaves the plate.

MSC:

74K20 Plates
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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