Nonlinear Surface Waves

University Of California-Davis, Davis CA

Investigators

Abstract

Surface waves are waves that propagate along a boundary or interface. They arise in many physical systems, such as water waves on the surface of the ocean and seismic surface waves generated by earthquakes. They also have a wide variety of technological applications, such as ultrasonic surface acoustic waves used in analog filters and surface plasmons used in optical and nano-optical devices. At lower intensities, effects of different waves add (waves superpose) and may be described by linear theories, but at higher intensities nonlinear effects become significant. Nonlinearity leads to qualitatively new phenomena, including wave interactions and the formation of singularities (such as shock waves). This project addresses the fundamental nonlinear dynamics of surface waves and their applications, especially nondispersive surface waves whose phase speed or frequency is independent of their wavelength. As a part of the project, graduate and undergraduate students will be trained through involvement in the research. The project will carry out an asymptotic analysis of nonlinear surface waves in a variety of physical systems. Applications will be made to electromagnetic surface waves, or surface plasmons, waves on vorticity discontinuities and surface quasi-geostrophic fronts, plasma waves, and Rayleigh waves in elasticity. The resulting asymptotic equations are typically spatially nonlocal and quasilinear. These equations will be studied analytically and numerically, in particular with the aim of understanding the nonlinear focusing and possible formation and propagation of singularities in these surface waves. In addition, the project will study the diffraction and glancing Mach reflection of shock waves, together with related problems in transonic aerodynamics.