Cyclostationary analysis of periodically forced turbulent jets*

The forcing of turbulent flows is ubiquitous, from airfoil drag reduction to jet noise suppression. However, the mechanisms by which the forcing alters the turbulence are poorly understood. Recently, various statistically based tools (for example, POD, SPOD) have been successfully employed to study the effect of the forcing on the turbulence in these flows. However, in many forced flows, in addition to the strong deterministic tonal response, the underlying stochastic turbulence is modulated by the applied forcing and thus deviates from the stationarity assumption invoked in these analyses. We explore several strongly periodically forced turbulent jets using the cyclostationary framework that, while used heavily in signal processing and mechanics, is relatively unknown by the turbulence community. The cyclostationary framework provides a natural extension that allows for the statistics to vary periodically in time. Using several cyclostationary tools, including the Wigner-Ville spectrum and degree of cyclostationarity measure, we investigate how the statistics are modified as a function of the phase of the forcing and to what degree forced turbulence is cyclostationary.