On the condition of streak formation in a bounded turbulent flow

Abstract

Flow between two surfaces at which no-slip and free-slip conditions can be imposed has been investigated numerically with a Fourier–Chebyshev pseudospectral method. Different mean shear rates have been applied to each boundary to study the effect of shear and boundary condition on the streaky structures that have been observed near walls in many previous investigations. In addition to the streaks found near the no-slip wall, the computations also reveal streaky structures when the free-slip surface is under a sufficiently high shear. The low-speed streaks observed near the free-slip surface, although appearing somewhat more pronounced, have much the same characteristics as the wall-layer streaks—e.g., the average spanwise spacing between the streaks both near the wall and the free surface is about 100 when normalized by the kinematic viscosity and the appropriate shear velocity (at the wall or at the free-slip surface). The results show that shear is much more important than the nature of the boundary in determining the dominant flow structure, rather unexpected since vortex lines can attach at a free-slip boundary whereas they cannot at a no-slip one. The formation of streaks appears to be governed by a local nondimensional shear parameter defined as S̃≡S‖〈u′w′〉‖/ε, where S is the mean shear rate, and 〈u′w′〉 and ε are the kinematic turbulent shear stress and rate of dissipation of turbulent kinetic energy, respectively. It is found that S̃≂1.0 is the condition at which the elongated low-speed streaky regions first appear.