Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs

The role of "pseudo-plane-waves" in advected acoustics under non-uniform conditions

Saul Abarbanel

Tel-Aviv University

Plane wave solutions in uniform flows and media are often presented as a propagator [exp iw(t - x - y)] multiplied by a constant coefficient – vector. When conditions are not uniform the linearized Euler (Navier-Stokes) equations do not admit plane waves solutions. We propose in such cases to use non-constant vectors to “drive” the propagators. We designate such solutions as “pseudo-plane-waves”. Two examples are presented where this approach allows us to obtain analytic solutions, namely the case of wave propagation in the terrestrial atmosphere and in shear flow.