Control of weak perturbations

Abstract

We define sound as being a weak perturbation in the properties of material consistent with the Navier-Stokes and continuity equations. Lighthill’s pioneering paper on aerodynamic noise gives an exact theory that enables interesting connections to be made between flow and sound. Aerodynamic noise being caused by quadrupoles is a good point of view, but what caused the quadrupoles? Were they possibly initiated by sound? Conclusions deduced from such a theory are not necessarily helpful, but they are true and might be very helpful indeed. The linear perturbations we call sound obey linear rules and it can be suppressed by anti-sound, a subject now becoming both practical and useful. The same must apply to any weak perturbation of a dynamic system perturbed from rest. Some perturbations are unstable and grow exponentially in their early weak state. They might be eliminated altogether by suppressing their linear form. The Rijke tube experiment shows that to be practical and shows also the close similarity that exists between acoustics and control theory. The lecture will give more examples of that type and suggest others that have yet to be demonstrated.