Carbon black set to reach 195 000 tonnes in 2001

Abstract

A nonlinear time-domain numerical model based on a body-exact approach is applied to study the problem of large amplitude motion of a tightly moored submerged sphere. In this model, the exact body condition on the instantaneous wetted body surface is satisfied as well as the linear condition on the still water surface. Numerical simulations were carried out for two wave steepness, each with various incident wave frequencies. It was found that for a smaller wave steepness, the oscillation frequency of the sphere is always the same as the wave frequency, while for a larger steepness, the sphere may oscillate with a large amplitude at the frequency that is half of the incident waves. The linear model satisfying both the linearized boundary conditions on the mean body surface and still water surface fails to capture this significant nonlinear phenomenon. This phenomenon is induced by a self-amplifying process in which the wave frequency potential and half-wave frequency body motion generate a half-wave frequency nonlinear wave force, while the half-frequency force in turn enhances the half-wave frequency motion.