Perturbation Problems in Fluid Dynamics.
Abstract
Perturbation methods and numerical methods were employed to study four problem areas in fluid dynamics. The areas and the progress were: (1) Viscous vortical flows - We showed how to combine the asymptotic theory and experiments to study slender vortex filaments and how to specify the numerical parameters needed for the vortex element method to predict correctly the motion of slender filament(s) in space. We presented formulas relating a rotational flow outside a sphere to the rotational flow in space and formulas defining the far-field sound. These formulas were used to study the interaction of a vortex filament with a sphere. (2) Shock wave interactions - A canonical nonlinear elliptic problem was formulated and used to correct the defect of linear theory near a singular ray where a weak shock interacts with a diffracted wave. A similar canonical problem was formulated to solve the interaction of a weak expansion wave with a diffracted wave. (3) Wave propagation - Rules were formulated for determining the multiplicity of acoustic signals and the retarded times for media moving with unsteady speed ranging from subsonic to supersonic. In the analysis of structural/acoustic interactions, the solution for the panel oscillation was uncoupled from the acoustic field by the formulation of the on surface conditions taking into account the acoustic effect. (10) Free boundary problems - We obtained solutions for the formation of a drop after the breaking up of symmetric slender jets or thin sheets. (AN)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 26, 1996
- Accession Number
- ADA305678
Entities
People
- Lu Ting
Organizations
- New York University