Fundamental solution of the problem describing ship motion in waves

Jan Jankowski

Abstract. The problem describing a ship motion in waves comprises the Laplace equation, boundary condition on wetted surface of the ship, condition on the free surface of the sea in the form of a differential equation, the radiation condition, and a condition at infinity. This problem can be transformed to a Fredholm equation of second kind, and then numerically solved using the boundary element method, if the fundamental solution of the problem is known. This paper presents the derivation of the fundamental solution. In physical interpretation, the fundamental solution represents the moving and pulsating source under free surface of the sea. The free surface elevation, generated by the source for different forward speed and frequency of pulsation, is presented in this paper.

Keywords: ship hydrodynamics, boundary value problem, free surface potential flows, fundamental solution.

Mathematics Subject Classification: 35J05, 35J25, 76B07, 76B20, 35R35.

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