Nonlinear Acoustics in a Dispersive Continuum: Random Waves, Radiation Pressure, and Quantum Noise.
Abstract
The nonlinear interaction of sound with sound is studied using dispersive hydrodynamics which is derived from a variational principle and the assumption that the internal energy density depends on gradients of the mass density. The attenuation of sound due to nonlinear interaction with a background is calculated and is shown to be sensitive to both the nature of the dispersion and decay bandwidths. The theoretical results are compared to those of low temperature helium experiments. A kinetic equation which describes the nonlinear self-interaction of a background is derived. When a Debye-cutoff is imposed, a white noise distribution is shown to be a stationary distribution of the kinetic equation. Zero point motion is introduced into the classical hydrodynamics through a renormalization scheme, which imposes the requirement that in a sound scattering the zero point motion does not lose energy. The form of the zero point motion is then determined by the kinetic equation and a derived fluid law that is analogous to Wien's displacement law for electromagnetic radiation. The kinetic equation with zero point motion included is shown to have a Planck distribution as a stationary solution. An H-theorem is presented. The attenuation and spectrum of decay of a sound wave due to nonlinear interaction with zero point motion is calculated. In one dimension, the dispersive hydrodynamic equations are used to calculate the Langevin and Rayleigh radiation pressures of wave packets and solitary waves. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1983
- Accession Number
- ADA127594
Entities
People
- Michael Anthony Cabot
Organizations
- University of California, Los Angeles