On acoustically modulated jet shear layers and the Nyquist–Shannon sampling theorem

Abstract

The goal of this paper is to present the behavior of a jet shear layer in response to acoustic excitation from a signal processing perspective. The main idea is that the vortices that roll-up in the jet shear layer are similar to the discrete samples of a digital control system, and, hence, that the Nyquist–Shannon sampling theorem should apply. We further hypothesize that the strength of a vortex is determined by the mean amplitude of the excitation waveform during its creation. We also argue that, at least in some cases, demodulation occurs as a result of the vorticity signal generated by the convection of discrete vortices past a point in the shear layer. This vorticity signal is related to the amplitude modulation (AM) excitation waveform by a half-wave rectification operation, a common implementation of an AM demodulator. To investigate these ideas, a free, round jet that is excited upstream of the nozzle is studied using particle image velocimetry. Experiments are conducted that confirm that the sampling theorem applies, and an aliased response is observed when the Nyquist limit is exceeded. Previous authors have attributed demodulation to a vortex merging mechanism, but we demonstrate that merging is not always required for demodulation and suggest that it is one of two mechanisms at play.