Articles | Volume 14, issue 4
Research article
08 Apr 2014
Research article |  | 08 Apr 2014

Non-linear water waves generated by impulsive motion of submerged obstacles

N. I. Makarenko and V. K. Kostikov

Abstract. A fully non-linear problem on unsteady water waves generated by an impulsively moving obstacle is studied analytically. Our method involves reduction of the Euler equations to the integral-differential system for the wave elevation together with normal and tangential fluid velocities at a free surface. Exact model equations are derived in explicit form in a case where an isolated obstacle is presented by a totally submerged elliptic cylinder. A small-time asymptotic solution is constructed for a cylinder which starts with constant acceleration from rest. It is demonstrated that the leading-order solution terms describe several wave regimes such as the formation of non-stationary splash jets by vertical rising or vertical submersion of the obstacle; the generation of diverging waves is also observed.

Final-revised paper