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_ci.e., RϜ√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.