A surface gravity wave superimposed upon a large scale flow is blocked at the point where the group velocity balances the convection by the large scale flow. The blockage phenomenon was investigated by Shyu and Phillips (1990) using a multiple-scale technique in which the monochromatic deep water short wave is treated linearly and the underlying non-uniform but slowly varying large scale flow is assumed to be steady in time. The technique provides a uniformly valid second-order ordinary differential equation in surface elevation from which a consistent solution is obtained by using a treatment suggested by the result of Smith (1975). In this study, the result of Shyu and Phillips (1990) is extended to investigate the interaction of a random wave train with an adverse current. Explicit expression of the frequency spectrum of the random wave train is obtained in terms of that specified in the region where no current is present.
It is known that when a wave encounters a non-uniform current, its characteristics undergo changes. If the current is in the direction of the wave and divergent, the wave amplitude decreases and the wave length increases. On the other hand, if the current is opposite to the direction of wave propagation and convergent, the wave amplitude increases and the wave length decreases; the wave becomes steeper and the sea choppier. In the event that the current is in the direction opposite to the wave, all theories recognize that there exists a current velocity referred to as stopping velocity, or a point in space, referred to as blockage point, where no energy of a wave of specified frequency can propagate further upstream. Most accounts predict a singularity in wave amplitude at the blockage point and assume that the wave breaks before reaching that point.