A flat ship theory on bow and stern flows

Abstract

An analytical solution of a two-dimensional bow and stern flow model based on a flat ship theory is presented for the first time. The flat ship theory is a counterpart to Michell's thin ship theory and leads to a mixed initial-boundary value problem, which is usually difficult to solve analytically. Starting from the transient problem, we shall first show that a steady state is attainable at the large time limit. Then the steady problem is solved in detail by means of the Wiener-Hopf technique and closed-form far-field results are obtained for an arbitrary hull shape. Apart from providing a better understanding of the underlying physics, the newly found analytical solution has shed some light on solving a longtime outstanding problem in the engineering practice of ship building, the optimisation of hull shape.

Steady free-surface flow at the stern of a ship

“…Stern flows with very small waves or that are completely wave-free have been generated by varying flow parameters or the precise geometry of the stern in the case of infinite depth fluid. 1, [3][4][5][6]8 In finite depth fluid waveless supercritical flows 9,[11][12][13][14] have been investigated as well, and recently, Maleewong and Grimshaw 10 obtained a waveless nonlinear solution for supercritical flow past a semi-infinite flat plate. However, less attention has been paid to smoothly detaching waveless subcritical flows in finite depth fluid.…”