A cylindrical wave-maker problem in a liquid of finite depth with an inertial surface in the presence of surface tension

TLDR: In this article, the problem of generating waves in a liquid of uniform finite depth with an inertial surface composed of a thin but uniform distribution of disconnected floating particles, due to forced axisymmetric motion prescribed on the surface of an immersed vertical cylindrical wavemaker of circular cross section under the influence of surface tension at the inertial surfaces, is discussed.

Abstract: The problem of generation of waves in a liquid of uniform finite depth with an inertial surface composed of a thin but uniform distribution of disconnected floating particles, due to forced axisymmetric motion prescribed on the surface of an immersed vertical cylindrical wave-maker of circular cross section under the influence of surface tension at the inertial surface, is discussed. The techniques of Laplace transform in time and the modified Weber transform involving Bessel functions in the radial coordinate have been employed to obtain the velocity potential. The steady-state development to the potential function as well as the inertial surface depression due to time-harmonic forced oscillations of the wave-maker are deduced. It is found that the presence of surface tension at the inertial surface ensures the propagation of time-harmonic progressive waves of any angular frequency.