Turbulent flow in pipes and channels as cross-stream inverse cascades of vorticity

A commonplace view of pressure-driven turbulence in pipes and channels is as cascades of streamwise momentum toward the viscous layer at the wall. We present in this paper an alternative picture of these flows as inverse cascades of spanwise vorticity in the cross-stream direction but away from the viscous sublayer. We show that there is a constant spatial flux of spanwise vorticity due to vorticity conservation and that this flux is necessary to produce pressure drop and energy dissipation. The vorticity transport is shown to be dominated by viscous diffusion at distances closer to the wall than the peak Reynolds stress, well into the classical log layer. The Perry-Chong model based on representative hairpin/horseshoe vortices predicts a single sign of the turbulent vorticity flux over the whole log layer, whereas the actual flux must change sign at the location of the Reynolds-stress maximum. Sign reversal may be achieved by assuming a slow power-law decay of the Townsend eddy-intensity function for wall-normal distances greater than the hairpin length scale. The vortex-cascade picture presented here has a close analog in the theory of quantum superfluids and superconductors, the phase slippage of quantized vortex lines. Most of our results should therefore apply as well to superfluid turbulence in pipes and channels. We also discuss issues about drag reduction from this perspective. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3013635]