Numerical study of generalized interfacial solitary waves

In a two-fluid system where the lower fluid is bounded below by a rigid bot tom and the upper fluid is bounded above by a free surface, two kinds of so litary waves can propagate along the interface and the free surface, classi cal solitary waves characterized by a solitary pulse or generalized solitar y waves with in addition nondecaying oscillations in their tails. In this p aper, we present numerical solutions of generalized solitary waves. Since g eneralized solitary waves cannot be obtained as the continuous limit of lon g waves, we in fact compute generalized long waves. The effects of capillar ity an neglected. The solutions depend on four dimensionless parameters, th e layer thickness ratio, the density ratio, the Froude number, and the dime nsionless amplitude of the oscillations in the far field. If the amplitude of the oscillations is varied while the other three parameters are kept fix ed, two limiting cases are conjectured. As the amplitude of the oscillation s decreases towards zero, it reaches a minimum nonzero value, which is expo nentially small. On the other hand, as the amplitude of the oscillations is increased, the generalized solitary wave eventually becomes a periodic wav e. In other words, the oscillations in the far field grow as large as the s olitary pulse. (C) 1999 American Institute of Physics. [S1070-6631(99)04006 -4].