Interaction between Short Surface Waves and Long Internal Waves

Abstract

The interaction between short surface waves and long internal waves in a two layer fluid has been investisated by a multiple scale method. When the group velocity of surface waves is equal to the phase velocity of internal wave, the steady solutions that represent the envelope of surface wave group and the internal wave coupling strongly with each other and moving with the same speed have been obtained. According to the relative magnitude of amplitudes of short and long waves, too different cases, namely, (1) a l / a s =0( e ), (2) a l / a s =0(1), where a l , a s are amplitudes of long and short waves respectively, have been analysed individually.