Wave propagation in advected acoustics within a non-uniform medium under the effect of gravity精品.pdf

Applied Numerical Mathematics 93 (2015) 61–68 Contents lists available at ScienceDirect Applied Numerical Mathematics /locate/apnum Wave propagation in advected acoustics within a non-uniform medium under the effect of gravity S. Abarbanel, A. Ditkowski ∗ School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel a r t i c l e i n f o a b s t r a c t Article history: We investigate linear wave propagation in non-uniform medium under the influence of Available online 28 April 2014 gravity. Unlike the case of constant properties medium here the linearized Euler equations do not admit a plane-wave solution. Instead, we find a “pseudo-plane-wave”. Also, there Keywords: is no dispersion relation in the usual sense. We derive explicit analytic solutions (both for Wave propagation Acoustic waves acoustic and vorticity waves) which, in turn, provide some insights into wave propagation in the non-uniform case. Vorticity waves © 2014 IMACS. Published by Elsevier B.V. All rights reserved. 1. Introduction The understanding of wave propagation is of great interest in several areas of science and technology, such as geophysics, electromagnetism, and in particular advected acoustics. Rarely can one obtain analytic solutions to such problems. Good computational approaches try to be guided as much as possible by analytic knowledge of the