Abstract:
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. |