Ploughing flows

A semi-infinite body, modelling the leading edge of a cutting tool or subme rged hydrofoil, lies beneath a free surface in a uniform stream of infinite ly-deep inviscid incompressible fluid flowing steadily under gravity. The b ody has horizontal upper and lower surfaces. The oncoming how is partly div erted over, and partly under the body. The flow in that portion that travel s over the body can be supercritical or subcritical. When it is supercritic al it approaches a stream of some (to be determined) speed in a channel of some (to be determined) depth. When it is subcritical, there is also a trai n of waves on that stream, whose amplitude is also to be determined. Semi-a nalytic high-speed and low-speed solutions are obtained, and a numerical so lution for finite speeds. There is a 'forbidden' intermediate speed range, within which steady how may not be possible.