Multiscale edge detection and imperfect phase synchronization of the wall turbulence

Abstract

Multiscale edge detection wavelet analysis is applied to the fluctuating velocity field obtained by direct numerical simulations of a fully developed turbulent channel flow at the Reynolds number based on the shear velocity, Re _τ=180. The wavelet coefficients are rewritten using analytic signal approach to sort out their local amplitudes and wavenumbers. Large zones of approximate constant wavenumbers have been identified at different scales, and a parallelism is constructed between these observations and stochastic synchronization phenomena. The results that we analyze strongly suggest that the wall turbulence is chaotically synchronized with the force induced by convecting coherent vortices near the wall, thus comforting our earlier results based on experimental velocity and wall shear stress time series. The spatial extend of phase-locked, synchronized zones feature a clear type-I intermittency behavior. The local amplitude intermittency in the synchronized zones is low, and the small-scale amplitude intermittency increases significantly when they are suppressed. The type-I intermittency disappears in the viscous and log layers.

Keywords:

• wall turbulence
• chaos
• chaotic synchronization
• wavelets
• wavelet analytical signal
• unstable periodic orbits
• intermittency
• coherent structures