Sensitivity of wavepackets in jets to nonlinear effects: the role of the critical layer

Abstract

Linear instability waves, or wavepackets, are key building blocks for the jet-noise problem. It has been shown in previous work that linear models correctly predict the evolution of axisymmetric wavepackets up to the end of the potential core of subsonic turbulent jets. Beyond this station, linear models fail, and nonlinearity is the likely missing piece. The essential underlying nonlinear mechanisms are unknown, and it remains unclear how these should be incorporated in a reduced-order model. The nonlinear interactions are considered in this work as an ‘external’ harmonic forcing added to the standard linear model. This modelling framework is explored using a locally parallel resolvent analysis to determine optimal forcing and associated responses, and a global approach based on 4D-Var data assimilation aimed at finding the optimal forcing of the parabolised stability equations that would minimise errors in the predictions of wavepackets. In all of the problems considered, the critical layer is found to be relevant: it is the position where sensitivity of wavepackets to nonlinearity is greatest. It is seen that disturbances are forced around the critical layer, and tilted by shear as they are advected, in a manner suggestive of an Orr-like mechanism. The ensemble of results suggests that critical-layer effects play a central role in the dynamics of wavepackets in subsonic turbulent jets, and that inclusion of such effects may remedy the shortcomings of linear reduced-order models.