A stochastic SPOD-Galerkin model for broadband turbulent flows

Abstract

The use of spectral proper orthogonal decomposition (SPOD) to construct low-order models for broadband turbulent flows is explored. The choice of SPOD modes as basis vectors is motivated by their optimality and space-time coherence properties for statistically stationary flows. This work follows the modeling paradigm that complex nonlinear fluid dynamics can be approximated as stochastically forced linear systems. The proposed stochastic two-level SPOD-Galerkin model governs a compound state consisting of the modal expansion coefficients and forcing coefficients. In the first level, the modal expansion coefficients are advanced by the forced linearized Navier-Stokes operator under the linear time-invariant assumption. The second level governs the forcing coefficients, which compensate for the offset between the linear approximation and the true state. At this level, least squares regression is used to achieve closure by modeling nonlinear interactions between modes. The statistics of the remaining residue are used to construct a dewhitening filter that facilitates the use of white noise to drive the model. If the data residue is used as the sole input, the model accurately recovers the original flow trajectory for all times. If the residue is modeled as stochastic input, then the model generates surrogate data that accurately reproduces the second-order statistics and dynamics of the original data. The stochastic model uncertainty, predictability, and stability are quantified analytically and through Monte Carlo simulations. The model is demonstrated on large eddy simulation data of a turbulent jet at Mach number $M=0.9$ and Reynolds number of $R{e}_D\approx 10^6$.

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• Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
• Spectral analysis of jet turbulence
• Frequency-time analysis, low-rank reconstruction and denoising of turbulent flows using SPOD
• Data-driven non-Markovian closure models
• Color of turbulence
• The ROMES method for statistical modeling of reduced-order-model error
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Cited by in corpus (4)

• Frequency-time analysis, low-rank reconstruction and denoising of turbulent flows using SPOD
• Spectral Proper Orthogonal Decomposition using Multitaper Estimates
• Neural-network learning of SPOD latent dynamics
• Analysis of coherence in turbulent stratified wakes using spectral proper orthogonal decomposition