The general problem of a two-dimensional water-solid impact is considered. The method of matched asymptotic expansions is used to solve the resulting boundary value problem for small penetration depth. The first-order solution obtained extends the classical Von Ka´rma´n and Wagner theories to non-normal impact and initially curved free surfaces. It accounts for nonlinear features such as the creation of a jet at each waterline. The application of the method to the computation of the impact loads exerted by spilling breakers on a marine structure is discussed.
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R Cointe (1989) studied this question.