Abstract
In this paper an estimate is made of the energy absorbed by wave motion at the interface of two superposed fluids when a body passes from one fluid to the other. The fluids are supposed perfect, incompressible, and bounded only by the interface, and axiβsymmetric and symmetrical twoβdimensional cases are considered. The body is supposed to move vertically and approach the interface from a great distance, and after crossing the interface to recede to a great distance, the speed being kept steady throughout. It is assumed that there were no waves originally present at the interface and that no splashing occurs during the crossing. The linear approximation to irrotational waves is used at the interface, and the slender body approximation is used at the boundary of the body. Transform methods are used to solve the Laplace equation for the velocity potential. Expressions are found for the waves set up as the body crosses the interface, and the energy used to generate the waves is found from a calculation of the work done against the wave resistance. The wave energy may be regarded as the sum of the wave energies for two cases : one in which the density difference between the two fluids is small, and another, in which the density of the upper fluid is zero. For the special cases of a spheroid and a spindleβshaped body, curves are shown of the wave energy against a dimensionless form of the inverse speed. Criteria are given for when maximum wave energy is developed for a thermal, and an estimate of this energy is made. This is done in Section 6.