A Parametric and Feasibility Study for Data Sampling of the Dynamic Mode Decomposition: Spectral Insights and Further Explorations

TL;DR

This study explores the sampling strategies and spectral properties of Dynamic Mode Decomposition (DMD) in turbulent flows, providing guidelines for optimal data collection, variable selection, and order reduction to improve DMD analysis accuracy.

Contribution

It offers a comprehensive parametric analysis of DMD sampling, spectral discretization, and variable selection, with practical recommendations for fluid dynamics applications.

Findings

Universal convergence states are confirmed for all DMD implementations.

Sampling range and resolution critically influence spectral discretization.

Optimal variables include static pressure and vortex identification criteria.

Abstract

This work continues the parametric investigation on the sampling nuances of the Dynamic Mode Decomposition (DMD) under the Koopman analysis. Through turbulent wakes, the investigation corroborated the generality of the universal convergence states for all DMD implementations. It discovered the implications of sampling range and resolution -- the determinants of the spectral discretisation by discrete frequency bins and the highest resolved frequency, respectively. The work reaffirmed the necessity of the Convergence state for sampling independence, too. Results also suggested that the observables derived from the same flow may contain dynamically distinct information, thus altering the DMD output. The static pressure and vortex identification criteria are optimal variables for characterising structural response and fluid excitation. The pressure, velocity magnitude, and turbulence kinetic energy fields also suffice for general applications, but the Reynolds stresses and velocity components shall be avoided. Mean-subtraction is recommended for best approximations of the Koopman eigen tuples. Furthermore, the parametric investigation on truncation discovered some low-energy states that dictate a system's temporal integrity. The best practice for order reduction is to avoid truncation and employ dominant mode selection on a full-state subspace, though large-degree truncation supports fair data reconstruction with low computational cost. Finally, this work demonstrated the synthetic noise resulting from pre-decomposition interpolation. In unavoidable interpolations to increase the spatial dimension n, high-order schemes are recommended for better retention of the original dynamics. Finally, the observations herein, derived from inhomogeneous anisotropic turbulence, offer constructive references for DMD on fluid systems, if not also others beyond fluid mechanics.