Stochastic synchronization of the near wall turbulence

Abstract

We investigate the characteristics of the instantaneous phases and amplitudes of the wavelet coefficients applied to the fluctuating wall shear stress and longitudinal velocity in the low buffer layer of a fully developed turbulent boundary layer. We show that the instantaneous phase exhibits long quiescent periods of constant values separated by sudden phase jumps. We establish a similarity with the stochastic synchronization of chaotic systems in the presence of noise that plays a role similar to the incoherent turbulence. We analyze the statistical characteristics of the constant phase periods and show the existence of type-I intermittency of the constant phase lengths related to a saddle-node bifurcation of the unstable periodic orbit embedded in the wall turbulent attractor. The period of the later is closely related to that of the cyclic regeneration of shear stress producing eddies.