On the Origin of Streaks in Turbulent Shear Flows

Abstract

It is shown that the ideas of selective amplification and direct resonance, based on linear theory, do not provide a selection mechanism for the well-defined streak spacing of about 100 wall units (referred to as 100⁺ hereafter) observed in wall-bounded turbulent shear flows. For the direct resonance theory (Benney & Gustaysson, 1981; fang et al., 1986), it is shown that the streaks are created by the nonlinear self-interaction of the vertical velocity rather than of the directly forced vertical vorticity. It is then proposed that the selection mechanism must be inherently nonlinear and correspond to a self-sustaining process. The streak formation is only one stage of the complete mechanism and cannot be isolated from the rest of the process. The 100⁺ value should be considered as a critical Reynolds number for that self-sustaining mechanism. For the case of plane Poiseuille flow the 100⁺ criterion corresponds to a critical Reynolds number of 1250, based on the centerline velocity and the channel half-width, which is close to the usually quoted value of about 1000. In plane Couette flow, it corresponds to a critical Reynolds number of 625, based on the half velocity difference and the half-width.