Coherent structure extraction in turbulent channel flow using boundary adapted wavelets

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.