Steady waves generated by a moving body and wave drag

Abstract

We consider a system of nonlinear periodic waves with wavelength λ. The waves move in a fluid from the right to the left with a constant phase velocity c above a flat horizontal bottom, the gravitational acceleration being g. The fluid is assumed to be perfect and incompressible. The motion is perceived to be two-dimensional and vortex-free. We introduce a coordinate system Oxy moving together with the waves in which the flow is steady. The x-axis is aligned with the bottom, and the y-axis is directed vertically upwards so that it intersects one of the wave crests. As may be inferred from dimensional analysis, a steady flow is determined by two dimensionless parameters. We denote these parameters as α and β (generally speaking, their specific choice is not of principle importance). We consider the wave shape and the velocity field to be known for the steady motion. The question arises as to whether it is possible to determine the phase velocity c of the wave motion from these data? Since the physical condition for determining c is absent, this cannot be done in general.