Nonlinear Wave Propagation

University Of California-Davis, Davis CA

Investigators

Abstract

Abstract, Proposal 0309648, Hunter, University of California-Davis Title: Nonlinear wave propagation This project addresses fundamental and poorly understood issues in the theory of hyperbolic conservation laws,such as the ones that model compressible fluid mechanics. It also addresses problems in incompressible fluid mechanics and general relativity, and applies the results to a variety of important physical problems. A common theme of much of the proposed work is how nonlinearity leads to the formation and propagation of various kinds of singularities, such as shock waves in compressible fluids, or space-time singularities in general relativity. Specific topics proposed for study are the following: shock wave reflection; shock wave propagation in random media; nonlinear hyperbolic surface waves in elasticity and magnetohydrodynamics; the Prandtl boundary layer equations and vorticity wave, mean flow interactions in incompressible fluid mechanics; and the effect of nonlinearity on gravitational waves in general relativity. Waves (such as sound waves, seismic waves, light waves, quantum mechanical waves,or gravitational waves) are a central feature of many physical systems, from the atomic to the cosmological scales. At lower intensities, waves superpose and they may be described by linear theories, but at higher intensities nonlinear effects becomes significant, leading to qualitatively new phenomena (like shock waves and solitons). Nonlinear waves are much more difficult to analyse mathematically than linear waves, and are often of great practical importance. For example, shock waves form around aircraft that travel close to the speed of sound. One aim of this project is to study basic, but not fully understood, shock wave phenomena, such as their reflection from walls. Among other topics, the project also includes a study of nonlinear surface waves, such as the Rayleigh waves which are generated by earthquakes and are used in a variety of ultrasonic devices, and a study of the formation and propagation of space-time singularities in gravitational waves.