Surface gravity waves due to a moving body: Onset of wave resistance as a critical phenomenon

The onset of the wave resistance, R, via generation of surface gravity waves by a long body moving with a velocity V, is considered. We demonstrate that for a special shape of the disturbance moving uniformly with velocity V, the wave resistance R(V) has a well-defined threshold (perfect bifurcation) at the critical value V-c, i.e., R similar to root V - V-c for V > V-c, and equals zero for V < V-c. For arbitrary shape of a moving disturbance the bifurcation becomes imperfect. It results in a small nonzero R usually observed at 0 < V < V-c. Using this idea, we have succeeded in describing quantitatively experimental data on the wave resistance of ship models obtained by D.W. Taylor in 1908.