
Accession Number : AD0633979
Title : HIGH FREQUENCY SOUND ACCORDING TO THE BOLTZMANN EQUATION,
Corporate Author : COURANT INST OF MATHEMATICAL SCIENCES NEW YORK UNIV N Y
Personal Author(s) : Grad,Harold
Report Date : 15 FEB 1966
Pagination or Media Count : 47
Abstract : The boundary value problem of sound generated at an oscillating wall propagating into a half space is solved for a linear Boltzmann equation with a general cutoff intermolecular potential and an arbitrary boundary condition at the wall. For a small bounded domain (two walls closer than a mean free path) proof of the existence of a solution is relatively simple. In a half space the solution is proved to exist for sufficiently high frequency omega > omega sub o (omega sub o is comparable to the mean collision frequency). Asymptotic expressions show the disappearance of a conventional sound wave at high frequency. This is consistent with known results for a relaxation model of the Boltzmann equation and qualitative estimates for the actual Boltzmann equation based on the dominance of the continuous spectrum at high frequency. At a fixed arbitrary distance from the wall, the dominant high frequency disturbance consists of just those particles emitted by the wall, decreased by scattering, but without any compensating contribution from the creation term of the collision operator. (Author)
Descriptors : (*SOUND, PROPAGATION), (*MATHEMATICAL MODELS, SOUND), HIGH FREQUENCY, BOUNDARY VALUE PROBLEMS, PARTIAL DIFFERENTIAL EQUATIONS, GAS FLOW
Subject Categories : Numerical Mathematics
Acoustics
Fluid Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE