Wavepackets in Subsonic Turbulent Jets: a Dynamical System Analysis
Résumé
It is well established that turbulent jets are characterized by large coherent structures. Recent investigations have corroborated the strong hypothesis that these structure can be modeled as ansatz of the linearized Navier-Stokes equations; for this reason, these coherent structure are commonly referred to as wavepackets. Moreover, these solutions exhibit a remarkable spatio-temporal organization, as shown by Breakey et al. [1]. The present work aims at further investigating the temporal behaviour associated with these structures from a dynamical system perspective.Starting from the work by Breakey et al. [1], we consider the pressure measurements extracted at different locations along the streamwise direction from an experimental, iso-thermal jet issuing at Ma=0.6 and Reynolds number Re=5.7 x 10^5. At each of these locations, it is possible to extract the time-series related with the pressure fluctuations. We consider two datasets: i) the raw data extracted simultaneously at n=7 locations, associated with the axisymmetric Fourier modes; ii) the projection of the raw data on a basis of proper orthogonal modes resolved with n=22 points along the streamwise direction. The projection of the whole flow on these solutions provides a low-order representation of the temporal dynamics of the system. We apply a variety of non-linear signal-processing, nonlinear and linear system identification techniques in order to explore the dynamics (see Semeraro et al. [2]). In particular, we estimate the correlation and minimal embedding dimensions of the system. Moreover, linear and nonlinear system identification is applied for identifying surrogate models of the system. We show that nonlinear models are appropriate at characterizing the dynamics of the system only in relatively short window of assimilation of the system, and are not able to characterize the full dynamics of the system. The same strategy of identification can be applied for computing control-oriented models. We show that linear transfer function are sufficient at optimally capturing the behaviour of the input-output system; indeed, nonlinearities are found un-necessary when analyzing the system from the control design perspective.