Nonlinear Free-Surface Flow Around an Impulsively Moving Cylinder

Abstract

Nonlinear free-surface flow around an impulsively accelerating, vertical surface-piercing cylinder is investigated analytically. The exact solutions for the velocity potential and free-surface elevation are derived up to the third order by the small-time-expansion method. The hydrodynamic pressure acting on the cylinder wall is also obtained. A constant horizontal acceleration is considered to illustrate our theoretical results. It is found that, during the initial stage of this impulsive motion, no travelling free-surface waves are present. A surge of water appears on the upwind face and a depression forms on the down-wind face. The second-order free-surface elevation is singular along the contact line between the fluid surface and the cylinder surface. The nonlinear pressure distribution on the cylinder surface has been determined.