MCE Ph.D. Thesis Seminar

Jet noise reduction is an important goal within both commercial and military aviation.  Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts.  A particularly promising modeling approach centers on certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound.  The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field.  The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case.  This thesis contributes to two aspects of these models.  First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, significantly reducing the computational cost of the model.  The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations.  Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering.  Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets.  Specifically, we use ensembles of large-eddy-simulation data along with two data decomposition techniques to educe the actual forcing experienced by wavepackets in a Mach 0.9 turbulent jet.  Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition.  In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures.  Furthermore, the structures that do exist are largely uncorrelated with the acoustic field.  Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct forcing from nonlinear interactions amongst wavepackets is not a vital noise source mechanism.  This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the forces, a conclusion that has important implications for jet noise modeling.