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On Wave Interactions II. Explosive Resonant Triads in Fluid Mechanics
Author(s) -
Mahoney D. J.
Publication year - 1996
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1996964407
Subject(s) - gravitational singularity , explosive material , context (archaeology) , fluid mechanics , physics , mechanics , classical mechanics , nonlinear system , amplitude , wave propagation , flow (mathematics) , phase velocity , singularity , fluid dynamics , mathematical analysis , mathematics , geology , optics , quantum mechanics , chemistry , paleontology , organic chemistry
This paper considers the occurrence of explosive resonant triads in fluid mechanics. These are weakly nonlinear waves whose amplitudes become unbounded in finite time. Previous work is expanded to include interfacial flow systems with continuously varying basic velocities and densities. The first paper in this series [10] discussed the surprisingly strong singular nature of explosive triads. Many of the problems to be studied here will be found to have additional singularities, and the techniques for analyzing these difficulties will be developed. This will involve the concept of a critical layer in a fluid, a level at which a wave phase speed equals the unperturbed fluid velocity in the direction of propagation. Examples of such waves in this context are presented.