Multiscale model reduction for unsteady fluid flow

Abstract

This dissertation develops methods for constructing simplified models of unsteady fluid flows in regimes ranging from weakly nonlinear to fully turbulent. These models can provide valuable insights into the flow physics, as well as inexpensive surrogate models suitable for analytic study and controller design. The emphasis is on extending traditional methods using recent advances in data-driven modeling in a manner that preserves the interpretability and robustness of classical analysis. Throughout, the proposed methodological developments are critically evaluated against extensive computational fluid dynamics simulations and experimental wind tunnel observations representing a variety of fundamental features of unsteady flows. This work takes three distinct approaches to model reduction. First, a perspective of the fluid flow as a high-dimensional, dissipative dynamical system with emergent large-scale coherence leads to approximations in terms of low-dimensional nonlinear dynamics. These models can be derived by projection of the governing equations or sparse model discovery; in either case it is crucial to systematically account for the influence of unresolved degrees of freedom. Alternatively, in fully-developed turbulence the evolution of global integral quantities can be viewed as deterministic motion forced by incoherent fluctuations. The analogy with statistical mechanics cannot be made rigorous for turbulence, but an empirical method is developed to approximate these generalized Brownian motions from limited experimental data. Finally, the observation that the behavior of physical systems is often determined by a dominant balance between a small subset of physical mechanisms motivates the development of an algorithm for objective identification of regions with different active physics. Underlying all of these frameworks is a unifying perspective of the flow as a system with complex nonlinear interactions across a wide range of spatiotemporal scales.