Effect of two-dimensional inhomogeneous flow on surface waves

Abstract

The evolution of a counterstream quasimonochromatic surface wave on a localized two-dimensional inhomogeneous perturbation of a current is investigated theoretically and experimentally. The model equation describing the surface wave field transformation has been derived and solved numerically. The time evolution of the initially homogeneous wave field when the flow perturbation arises at a certain moment of time is investigated. It is shown that in the case when the group velocity of surface waves is nearly equal and opposite to current velocity the even weak perturbations of current velocity modify appreciably the surface wave field. The dependence of the two-dimensional quasistationary pattern of the surface wave field in the vicinity of the inhomogeneous flow domain on the wavelength of the surface wave and the angle between the surface wave vector and the current velocity is investigated. It is found that there are definite directions (at angle /spl sim/55 degrees to the current velocity) where the main variations of the surface wave field occur. The space dimensions of the domain, where the wave field transformation is essential, greatly exceed the space dimensions of the localized flow perturbation. The growth rate of the wave field perturbation decreases as the group velocity of surface waves tends to the current velocity. Qualitative interpretation of results of the numerical calculation is given. The theoretical results has been checked experimentally in laboratory tank.