Perturbation Problems in Fluid Dynamics.

Perturbation methods and numerical methods were employed to study five problem areas. 1 For viscous vortical flows, a complete account of the asymptotic analyses, numerical studies and their physical meaning was presented in Springer-Verlag Lecture Notes in 1991. An extension of the asymptotic analysis for the motion and diffusion of a slender vortex filament to allow for the variation of the core structure along the filament was accomplished in 1992. This extension was needed for the study of the vortex breakdown problem. 2 For shock wave interactions, the locations and the types of singularities in the interaction of semilinear waves in three- and higher dimensional space were identified. 3 For wave propagations in a bubbly liquid, a survey of the linear and nonlinear theories and their limitations was presented in an article in Advances in Applied Mechanics in 1991. A system of effective equations uniformly valid at small gas volume fraction and large bubble number density was derived in 1992. 4 For free boundary problems, solutions simulating the breaking up or merging of symmetric slender jets or thin sheets were obtained in 1990. The solution for drop formation after the breaking was formulated recently. 5 In the analysis of structuralacoustic interactions, the solution for the panel oscillation was uncoupled from that for the acoustic field by the recent formulation of the on surface conditions taking into account the acoustic effect.