Viscosity and Surface-Tension Effects on Wave Generation by a Translating Body

Abstract

Various theoretical and experimental studies have been carried out to examine the generation of waves ahead of a translating body. Not all issues pertaining to this wave-motion problem are, however, fully resolved. In particular, mechanisms pertaining to generation of white-water instability and inception of vortices in the bow region are not fully understood. In this paper, the two-dimensional, unsteady, nonlinear, viscous-flow problem associated with a translating surface-piercing body is solved by means of finite-difference algorithm based on boundary-fitted coordinates. Effects of surface tension and surfactants are examined. Results of this work resolve certain classic issues pertaining to bow flows. A continuous generation of short and steepening bow waves is observed at low (draft) Froude number, a nonlinear phenomenon uncovered recently in the case of inviscid fluid also. This indicates that, steady-state nonlinear bow-flow solution may not exist, even at low speed. It is postulated that these short bow waves are responsible for the white-water instability commonly observed ahead of a full-scale ship. The amplitudes of these short bow waves are suppressed by surface tension, which is, possibly, the reason why white-water instability is not distinctly observed in laboratory-scale experiments. The presence of surfactants on the free surface is found to intensify the generation of free-surface vorticity, thus resulting in the formation of bow vortices. The accumulation of surface-active contaminants at the bow is hence responsible for the generation of bow vortices observed in laboratory experiments at low Froude number. At high Froude number, an impulsive starting motion of the body results in the generation of a jet-like splash at the bow and a gentle start an overturning bow wave, as previously observed in the case of inviscid bow flow.