INTERMODAL INTERACTION OF INTERNAL SOLITARY WAVES

Interaction of internal solitary waves of different modes in an incompressible fluid with an exponential stratification in density is considered. Two such waves are considered. These waves may be going in the same direction or in opposite directions. The analysis shows that the interaction produces two pairs of waves, whose mode indices are the difference and the sum of those of the original waves, respectively. Each pair consists of a right-going wave and a left-going one, and a part that vanishes eventually everywhere. Higher-order terms affecting interaction are briefly discussed. The interaction of more than two waves can be dealt with pair by pair.