Mechanism of Roll-Streak Structure Formation and Maintenance in Turbulent Shear Flow

Abstract

In wall-bounded shear flow the primary coherent structure is the streamwise roll and streak (R-S). Absent of an associated instability the R-S has been ascribed to non-normality mediated interaction between the mean flow and perturbations. This interaction may occur either directly due to excitation of a transiently growing perturbation or indirectly due to destabilization of the R-S by turbulent Reynolds stresses. A fundamental distinction between the direct and the indirect mechanisms, which is central to understanding the physics of turbulence, is that in the direct mechanism the R-S is itself the growing structure while in the indirect mechanism the R-S emerges as a self-organized structure. In the emergent R-S theory the fundamental mechanism is organization by the streak of Reynolds stresses configured to support its associated roll by the lift-up process. This requires that a streak organizes turbulent perturbations such as to produce Reynolds stresses configured to reinforce the streak. In this paper we provide detailed analysis explaining physically why this positive feedback occurs and is a universal property of turbulence in shear flow. DNS data from the same turbulent flow as that used in the theoretical study (Poisseullle flow at R=1650) is also analyzed verifying that this mechanism operates in DNS.