Accession Number : ADA305678

Title :   Perturbation Problems in Fluid Dynamics.

Descriptive Note : Final rept. 1 Nov 92-31 Dec 95,

Corporate Author : NEW YORK UNIV NY COURANT INST OF MATHEMATICAL SCIENCES

Personal Author(s) : Ting, Lu

PDF Url : ADA305678

Report Date : 26 JAN 1996

Pagination or Media Count : 18

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)

Descriptors :   *SHOCK WAVES, *VORTICES, *ACOUSTIC FIELDS, MATHEMATICAL MODELS, SLENDER BODIES, ACOUSTIC WAVES, COMPUTATIONAL FLUID DYNAMICS, FAR FIELD, FLOW FIELDS, WAVE PROPAGATION, BOUNDARY VALUE PROBLEMS, ASYMPTOTIC SERIES, ACOUSTIC SIGNALS, PERTURBATIONS, SYSTEMS ANALYSIS, SUBSONIC FLOW, UNSTEADY FLOW, FLOW NOISE, NUMERICAL METHODS AND PROCEDURES, SUPERSONIC FLOW, VISCOUS FLOW, ACOUSTIC VELOCITY, NONLINEAR ALGEBRAIC EQUATIONS, PRESSURE DISTRIBUTION, JET FLOW.

Subject Categories : Acoustics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE