Kelvin and V-like ship wakes affected by surfactants

Synthetic aperture radar (SAR) ship wake images in light wind and calm sea conditions frequently appear in the form of a bright V with a half-angle of 2 to 3 deg. Sophisticated and conflicting explanations of this phenomenon, based on the Bragg scattering mechanism, have been proposed. There is a be lief that the narrow V-wake is not a part of the Kelvin wake. An alternativ e approach, which is not generally accepted, suggests that short divergent Kelvin waves may contribute to the V-wake imaging although these waves are mixed with unsteady surface waves generated by the ship-induced turbulence. Ship-generated divergent waves contaminated by surfactants and their radar backscattering cross section are studied. The hull of the ship is represen ted by a single layer of hydrodynamic singularities. The Green function of a point source moving below a free surface covered by surfactants is derive d. A closed-form asymptotic solution for the far ship wave wake is obtained . It is used to calculate analytically the corresponding radar backscatteri ng cross section. The radiative, viscous, and surfactant-induced decay of t he V-wake brightness along the V-arms is discussed. The theoretical results are compared against available experimental data.