Capillary gravity waves caused by a moving disturbance: Wave resistance

The dispersive property of capillary gravity waves is responsible for the complicated wave pattern generated at the free surface of a calm liquid by a disturbance moving with a velocity V greater than the minimum phase speed ${\mathit{c}}^{\min }$=(4gγ/ρ${)}^{1/4}$ (ρ is the liquid density, γ is the liquid-air surface tension, and g is the acceleration due to gravity). The disturbance may be produced by a small object immersed in the liquid or by the application of an external surface pressure distribution. The waves generated by the moving disturbance continually remove energy to infinity, and, consequently, the disturbance experiences a drag called the wave resistance. The wave resistance corresponding to a surface pressure distribution symmetrical about a point was analyzed by Havelock in the particular case of pure gravity waves (i.e., γ=0) for which the minimum phase speed reduces to zero. Here, we investigate the more general case of capillary gravity waves using a linearized theory. We also analyze the integral depression of the liquid, the momentum carried by the liquid, and the effective mass of the disturbance for velocities V smaller than ${\mathit{c}}^{\min }$. These results may possibly lead to a new method of probing soft surfaces. © 1996 The American Physical Society.