Coherent structure extraction in turbulent channel flow using boundary adapted wavelets

TL;DR

This paper introduces boundary adapted wavelets for analyzing turbulent channel flow, enabling separation of flow into coherent and incoherent parts while preserving key flow statistics and energy budgets.

Contribution

The authors develop isotropic boundary adapted wavelets for multi-resolution analysis and demonstrate their effectiveness in extracting coherent structures from turbulent flow data.

Findings

Coherent vorticity reconstructed from intense wavelet coefficients matches total flow statistics.

Thresholding wavelet coefficients effectively separates flow into coherent and incoherent components.

Energy and enstrophy spectra of coherent flow closely resemble total flow spectra.

Abstract

We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze direct numerical simulation data of turbulent channel flow computed at a friction Reynolds number of 395, and investigate the role of coherent vorticity. Thresholding of the vorticity wavelet coefficients allows to split the flow into two parts, coherent and incoherent vorticity. The coherent vorticity is reconstructed from their few intense wavelet coefficients. The statistics of the coherent part, i.e., energy and enstrophy spectra, are close to the statistics of the total flow, and moreover, the nonlinear energy budgets are very well preserved. The remaining incoherent part, represented by the large majority of the weak wavelet coefficients, corresponds to a structureless, i.e., noise-like, background flow whose energy is equidistributed.