Data‐driven identification of the spatiotemporal structure of turbulent flows by streaming dynamic mode decomposition

Abstract

Streaming Dynamic Mode Decomposition (sDMD) is a low‐storage version of dynamic mode decomposition (DMD), a data‐driven method to extract spatiotemporal flow patterns. Streaming DMD avoids storing the entire data sequence in memory by approximating the dynamic modes through incremental updates with new available data. In this paper, we use sDMD to identify and extract dominant spatiotemporal structures of different turbulent flows, requiring the analysis of large datasets. First, the efficiency and accuracy of sDMD are compared to the classical DMD, using a publicly available test dataset that consists of velocity field snapshots obtained by direct numerical simulation of a wake flow behind a cylinder. Streaming DMD not only reliably reproduces the most important dynamical features of the flow; our calculations also highlight its advantage in terms of the required computational resources. We subsequently use sDMD to analyse three different turbulent flows that all show some degree of large‐scale coherence: rapidly rotating Rayleigh–Bénard convection, horizontal convection and the asymptotic suction boundary layer (ASBL). Structures of different frequencies and spatial extent can be clearly separated, and the prominent features of the dynamics are captured with just a few dynamic modes. In summary, we demonstrate that sDMD is a powerful tool for the identification of spatiotemporal structures in a wide range of turbulent flows.

Symmetry-Reduced Low-Dimensional Representation of Large-Scale Dynamics in the Asymptotic Suction Boundary Layer

“…We extend on preliminary work on large-scale coherence in the ASBL [28], carried out on two-dimensional data obtained by streamwise averaging. Firstly, the analysis is now carried out on the full three-dimensional flow fields, hence an additional shift symmetry in streamwise direction must be accounted for.…”

Preface to special issue on direct numerical simulations of turbulent flows—Part I

“…This allows the generation of data sets resolved in space and time, which can be exploited to thoroughly test novel analysis and postprocessing methods. Yang et al [11] apply a streaming dynamic mode decomposition [1] to extract the dominant spatiotemporal patterns of a wake flow behind a cylinder, in rapidly rotating Rayleigh-Bénard convection, in classical horizontal convection, and in an asymptotic suction boundary layer. They found that structures of different temporal and spatial frequencies can be separated and that the most salient features of the dynamics can be generally captured with a small number of dynamic modes, thereby highlighting the capabilities of the method.…”

Preface to special issue on Direct numerical simulations of turbulent flows—Part II

“…For a brief introduction to DNS, the reader is referred to the preface of the preceding issue [1], and references therein. The two issues contain a broad spectrum of topics which includes the study of sound generation mechanisms in combustion [4], the extraction of dominant spatiotemporal patterns and coherent structures in several canonical flows [12,14], the active control of turbulence in compressible fluid flows [9], the modeling of jets impinging on rough surfaces [10], the high-order, low-dissipation modeling of compressible multi-phase flows [2] and the accurate simulation of particle-and bubble-laden fluid flows [3]. In what follows, we briefly summarize the three contributions to the second issue.Flows driven by pressure gradients and by temperature-induced buoyancy forces are referred to as mixed convection flows and are common in nature and in engineering, for example, in heat exchangers, cooling systems, and air-conditioned rooms and spaces, such as an airplane cabin.…”