Influence of Current on Statistical Properties of Waves

The influence of wave-current interactions on various wave statistics is examined analytically. The statistics considered are those of peak magnitude, numbers of zero crossings and maxima, velocities of zeros, specular points, and points of inflexion of sea surface. The sea surface is considered both as a function of space and time. The random wave field is assumed to be unidirectional, zero mean, Gaussian, stationary and homogeneous, and in deep water. The current is considered to be steady in time, nonuniform in space, uniformly distributed in depth, and in or opposite to the direction of the waves. Numerical results are obtained and presented graphically. Results indicate that the interactions phenomena have a relatively mild influence on the maxima of sea surface but the rate of zero crossings and maxima of sea surface, treated as function of space, and the velocity of zeros, specular points, and points of inflexion, are affected by the presence of current to an appreciable extent and can be utilized effectively for current measurements by remote sensing devices.