Interaction of random wave–current over uneven and porous bottoms

Abstract Starting from linear wave theory and applying Green’s second identity and considering wave–current interaction for porous bottoms and variable water depth, the comprehensive mild-slope equation model theory of wave–current interaction is developed, then paying attention to the effect of random waves, by use of Kubo et al.’s method, a model theory of the interaction between random waves and current over uneven and porous bottoms is established. Finally the characteristics of the random waves are discussed numerically from both the geometric-optics approximation and the target spectrum.