Advanced Fluid Mechanics - Low-Order Modeling for Turbulent Flow

Statistical analysis of turbulent flow data. Modal representations. Goals for low - order models, observability and controllability. Data-driven techniques: proper orthogonal decomposition (POD)/principal component analysis (PCA), spectral POD, dynamic mode decomposition, linear stochastic estimation, and their extensions. Disambiguating linear and nonlinear effects, sparse identification of nonlinear dynamics (SINDy), Koopman analysis, etc. Equation-driven models: eigenanalysis, pseudospectra, resolvent analysis. Connections between data-driven and equation-driven modeling approaches. Low-order models for turbulent flows. Prerequisites: Familiarity with turbulent flows (ME 361), or consent of the instructor.