Functional Analysis and Applications Seminar 

18/06/2010, 14:00 — 15:00 — Room P3.10, Mathematics Building
Börje Nilsson, Linnaeus University, Kalmar, Sweden

Mathematical modelling of acoustic waves interacting with unstable flows in waveguides

The effect on the propagation of acoustic waves, from a slow motion in the medium where the propagation occurs, is usually very small. An important exception is, however, when the mean flow of the motion is unstable. There could then be an interaction between the acoustic wave and the mean flow and this interaction could be strong. One such instability occurs when the mean flow separates from a waveguide boundary at a sudden area expansion or the exit. The talk describes the formulation and solution of mathematical models describing the acoustic-flow interaction at such discontinuities. This formulation is of wave scattering nature and is solved with Wiener-Hopf techniques, which are particularly suited for the inclusion of unstable wave parts. Of particular importance is to classify the types of instabilities: a) convective instability, when the stationary solution exists and b) absolute instabilities when a stationary solution does not exist. For a particular model of the flow, the vortex sheet model, the stationary solution exists but is an ultra distribution. As an introduction to the talk, basic stability theory is recalled. At the end, predictions from simulations with the theory are presented together with confirming experimental results.