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

✍ Scribed by Yoshimasa Matsuno

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 119 KB
• Volume: 265
• Category: Article
• ISSN: 0375-9601
• DOI: 10.1016/s0375-9601(99)00910-x

✦ Synopsis

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 here 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 2D collapsing clusters.