Effects of currents on super- and sub-harmonic waves in a two-fluid system

Effects of currents on wave motions in a two‐fluid system are theoretically studied in this paper. Since super‐ and sub‐harmonic waves are naturally generated by the interaction of arbitrary linear waves, it is of theoretical and practical interest to investigate the influence of pure currents not only on linear waves, but also on second‐order waves. Solutions are derived using the perturbation technique. Solutions of internal Stokes waves recovered from present solutions are firstly discussed. Analyses of the super‐ and sub‐harmonic interactions are carried out for the deep‐ and shallow‐water configurations, respectively. Conditions resulting in the elimination of second‐order waves are determined. Present solutions include and unify most existing theories for the two‐ and single‐fluid systems, and are of great importance to the analysis of random internal waves.