Adjoint­-based analysis of controllability of turbulent jet noise

Past efforts have used optimal control theory, based on the numerical solution of the adjoint flow equations, to perturb turbulent jets to reduce radiated sound. These have been successful in that sound is reduced, with concomitant changes to large-scale turbulence structures in the flow. However, control remains challenged by the chaotic dynamics of the turbulence, which degrades smoothness of cost functional in control parameter space, thus limiting control effects to a relatively short time horizon. Wave packets can be a useful and relatively deterministic model for the large-scale noise mechanisms in jets. Using discrete-exact, dual-consistent adjoint gradients in conjunction with high-fidelity simulations, we assess the growth of sensitivity in time and general controllability. The most effective immediate control of a $M = 1.3$ jet is achieved with a control-time horizon of $32.4D/a_{\infty}$; longer or shorter time horizons prove less effective, which thus marks a balance between increasing authority through sensitivity and the disruptive influence of chaotic effect in the turbulence for this objective. After the control period, the rate at which the jet returns to its baseline louder state also presents a potentially important time scale for the flow and chaotic dynamics.