Peaked sloshing in a wedge container

Abstract

Finite-amplitude free-surface flow in a wedge container is investigated analytically. We study a motionless standing wave of pure potential-flow acceleration with maximal amplitude where its right-angle surface peak falls from rest. The nonlinear free-surface conditions are satisfied by a family of flows where the chosen initial acceleration field is governed by one single dipole plus its three image dipoles. Streamlines and isobars are plotted, with the free surface as the zero-pressure isobar. The key geometric parameters are tabulated for each case, supplied with force calculations for an upright wedge container. The present approach is assessed against established eigenfunctions for linearized standing waves in a wedge container. The present dipole flows constitute a much richer family of peaked free sloshing shapes than the classical Fourier modes of free oscillation.