Coherent structure extraction in turbulent channel flow using boundary adapted wavelets

^†This article is dedicated to Professor Javier Jimenez on the occasion of his 70th birthday.

ABSTRACT

We introduce boundary adapted wavelets, which are orthogonal and have the same scale in the three spatial directions. The construction thus yields a multiresolution analysis. We analyse 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 us to split the flow into two parts, coherent and incoherent flows. The coherent vorticity is reconstructed from its few intense wavelet coefficients and the coherent velocity is reconstructed using Biot–Savart's law. The statistics of the coherent flow, i.e. energy and enstrophy spectra, are close to the statistics of the total flow, and moreover, the nonlinear energy budgets of the total flow 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.

KEYWORDS:

• Turbulent channel flow
• coherent structure
• wavelet
• direct numerical simulation

Acknowledgements

We thank Professor Javier Jiménez for fruitful discussions about computing the mean pressure and the divergence issue. The computations were carried out on the FX100 systems at the Information Technology Center of Nagoya University. This work was partly supported by JSPS KAKENHI Grant Numbers (S) 24224003 and (C) 25390149. K.S. thankfully acknowledges financial support from ANR, contract SiCoMHD (ANR-Blanc 2011-045). Marie Farge and Kai Schneider acknowledge support by the French Research Federation for Fusion Studies within the framework of the European Fusion Development Agreement (EFDA).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

JSPS KAKENHI [grant number (S) 24224003], [grant number (C) 25390149]. ANR: Kai Schneider, contract SiCoMHD [grant number ANR-Blanc 2011-045]. French Research Federation for Fusion Studies within the framework of the European Fusion Development Agreement (EFDA): Marie Farge and Kai Schneider.