4aPA6. Nonlinearity versus diffraction within a focusing weak shock.

Session: Thursday Morning, May 16

Time: 9:15

Author: Andrew A. Piacsek
Location: Lawrence Livermore Natl. Lab., Univ. of California, P.O. Box 808, Livermore, CA 94551


In a classic paper treating the propagation of weak shocks, Whitham elucidated the process by which nonlinear effects would prevent rays within a concave portion of a shock front from intersecting, thereby avoiding a folded wavefront and associated caustics [G. B. Whitham, J. Fluid Mech. 1, 290--318 (1956)]. Whitham's analysis neglected the effects of diffraction arising from a finite shock thickness. When this length scale is small compared to that of the wavefront's curvature, Whitham's nonlinear correction to geometrical acoustics is a good model for the development of the shock front. When the length scales are comparable, as they are near the focal point, diffraction becomes important and acts both in conjunction with nonlinearity (to limit the shock amplitude) as well as against it (inhibiting the refraction of rays). Recent numerical studies [A. Piacsek, Ph.D. thesis, The Pennsylvania State University (1995)] indicate that the latter effect can lead to the formation of a folded wavefront, bounded by caustics, just as linear geometric theory predicts. The present paper addresses quantitatively how the relative importance of nonlinearity and diffraction (as represented by the shock amplitude, thickness, and wavefront curvature) determines the behavior of a focusing weak shock. [Work performed by the Lawrence Livermore National Laboratory under U. S. Department of Energy Contract No. W-7405-ENG-48.]

from ASA 131st Meeting, Indianapolis, May 1996