Influence of two-dimensional nonuniform currents on surface waves

Transformation of quasi-monochromatic upstream surface waves propagating in a locally two-dimensional nonuniform perturbation of a current is investigated theoretically and experimentally. A model equation governing surface wave amplitude has been derived and solved numerically. The evolution of an initially uniform field of surface waves when the current is suddenly perturbed at an instant is studied within the framework of this equation. It is found that there are some distinguished directions, making an angle of about 55 with the current velocity, in which the main variations in surface-wave amplitude occur. The spatial size of the region where the transformation of surface waves is substantial is much greater than the spatial size of the localized perturbation of the current. The theoretical model was examined experimentally in a laboratory tank. The nonuniform current was created by a flow over an ovaloid and may be considered to be two-dimensional and nonuniform near the water surface. The surface waves were generated by a mechanical wave generator. The two-dimensional distribution of surface-wave amplitudes was registered. The numerical computations of the distribution of surface-wave amplitudes performed specially for the experimental conditions have shown good agreement between experimental data and calculations.