Transverse instability and collapse of internal algebraic solitary waves in fluids of great depth

The effects of transverse perturbations on one-dimensional (1D) internal algebraic solitary waves are investigated on the basis of the 2D Benjamin-Ono equation. Applying Whitham's theory, we find that the 1D solitary waves are unstable in media with positive dispersion. We are particularly concerned hen with the long-term evolution of instabilities in the long-wave limit. We show that the Whitham modulation equations reduce to the model equations describing the nonlinear development of the Rayleigh-Taylor instability in a shallow layer of incompressible fluid, Analytical solutions to the modulation equations reveal that the transverse instability of 1D solitary wave results in the formation of 1D collapsing clusters. (C) 2000 Elsevier Science B.V. All rights reserved.