UC San Diego

The overarching goal of this dissertation is devising computational tools for high-Reynolds number, turbulent, realistic, engineering flows, then applying the tools as such. To meet this goal, the tools must be statistical. We therefore develop new statistical methods, each tailored to a distinct type of statistics. They range from an improved algorithm for spectral proper orthogonal decomposition (spectral POD, or SPOD), made for flows with stationary statistics and broadband--tonal spectra, called adaptive sine-taper SPOD; to a workflow that synthesizes time-varying mean-flow analysis and space--time POD, designed for statistically transient flows; to a wholly new method created for strongly nonlinear flows, named triadic orthogonal decomposition (TOD). We test the methods on a variety of turbulent examples, including an open-cavity flow, jets, a wind-turbine wake, and isotropic turbulence. The examples show that sine-taper SPOD balances sharply resolving tonal peaks and smoothly estimating broadband spectra. They show that the space--time workflow can tackle the finite-time turbulent statistics of a flow responding to forcing. And they show that TOD finds coherent structures which optimally capture triadic momentum transfer, distinguishes between a recipient, a donor, and a catalyst of energy transfer, quantifies their energy exchanges, recovers energy-conservation laws, and reveals where structures interact. The second part of this dissertation explores one flow in particular: large-eddy simulations (LES) of a supersonic jet from a twin-rectangular nozzle. The nozzle and flow conditions mimic those of tactical-aircraft engines, which emit harmful noise. We aim to understand the physics in order to control the jet and reduce its noise. When the jet is unforced, SPOD finds two flapping screech modes, high-amplitude noise sources. When it is periodically forced, one screech mode vanishes. We develop and apply a new variant of bispectral mode decomposition (BMD), uncovering a network of spatial-symmetry triads. We then investigate the feasibility of reinforcement learning (RL) for jet-noise reduction. Training on the jet, our RL agent learns slowly and unsteadily, because of LES's costliness and turbulent stochasticity. This highlights the need for model reduction before RL can control realistic simulated flows.