Data-driven feature identification and sparse representation of turbulent flows

Identifying coherent structures in fluid flows is of great importance for reduced order modelling and flow control. However, extracting such structures from experimental or numerical data obtained from a turbulent flow can be challenging. A number of modal decomposition algorithms have been proposed in recent years which decompose time-resolved snapshots of data into spatial modes, each associated with a single frequency and growth-rate. Most prominently among them is dynamic mode decomposition (DMD). However, DMD-like algorithms create an arbitrary number of modes. It is common practice to then choose a smaller subset of these modes, for the purpose of model reduction and analysis, based on some measure of significance. In this work, we present a method of post-processing DMD modes for extracting a small number of dynamically relevant modes. We achieve this through an iterative approach based on the graph-theoretic notion of maximal cliques to identify clusters of modes and representing each cluster with a single representative mode

Data driven feature identification and sparse representation of turbulent flows

dentifying coherent structures of fluid flows is of greatimportance for reduced order modelling and flow control.Finding such structures in a turbulent flow, however, canbe challenging. A number of modal decomposition algo-rithms have been proposed in recent years which decom-pose snapshots of data into spatial modes, each associatedwith a single frequency and growth-rate, most prominentlydynamic mode decomposition (DMD). However, the num-ber of modes that DMD-like algorithms construct may beunrelated to the number of significant degrees of freedomof the underlying system. This provides a difficulty if onewants to create a low-order model of a flow. In this work,we present a method of post-processing DMD modes forextracting a small number of dynamically relevant modes.This is achieved by first ranking the DMD modes, then us-ing an iterative approach based on the graph-theoretic no-tion of maximal cliques to identify clusters of modes and,finally, by replacing each cluster with a single (pair of)modes

Extrapolating statistics of turbulent flows to higher Re using quasi-steady theory of scale interaction in near-wall turbulence

A new technique for extrapolating statistical characteristics of near-wall turbulence from medium to higher Re is outlined. Results for extrapolating the velocity two-point correlation from Re τ = 2003 to Re τ = 4179 and for the parameters of an optimized comb probe for detecting the large-scale velocity component required for applying the technique in practice are presented

A large-scale filter for applications of QSQH theory of scale interactions in near-wall turbulence

An outlook on the recently proposed quasi-steady quasi-homogeneous (QSQH) theory of the effect of large-scale structures on the near-wall turbulence is provided. The paper focuses on the selection of the filter, which defines the large-scale structures. It gives a brief overview of the QSQH theory, discusses the filter needed to distinguish between large and small scales, and the related issues of the accuracy of the QSQH theory, describes the probe needed for using the QSQH theory, and outlines the procedure of extrapolating the characteristics of near-wall turbulence from medium to high Reynolds numbers