The FDR Prize

Abstract

From the 57 papers published in the year 2009 in Fluid Dynamics Research the following paper has been selected for the third FDR prize:'A driving mechanism of a turbulent puff in pipe flow' by Masaki Shimizu and Shigeo Kida, published in volume 41 (August 2009) 045501.Research on the pipe flow transition has a long history dating from Reynolds' experiment (1883) but the problem of critical Reynolds number (the lowest transition Reynolds number) has not yet been solved theoretically. The authors of this paper considered that one approach to solving the problem is to find nontrivial solutions of the Navier–Stokes equation for the lowest transition Reynolds number such as traveling wave solutions found in Couette flow, and focused on an equilibrium turbulent puff as a candidate for the nontrivial solutions. Through realizing an equilibrium state of a turbulent puff numerically by using a spectral code with high accuracy (which was developed by the authors), the authors proposed a self-sustenance mechanism of an equilibrium puff, in which development and breakdown of low-speed streaks play an important role.The proposed self-sustenance cycle of the equilibrium puff consists of the following processes. Turbulence in the puff generates low-speed streaks accompanied by streamwise vortices near the pipe wall, similarly to the regeneration cycle of near-wall turbulence. As a puff moves downstream, low-speed streaks are left upstream of the puff's trailing edge. On the laminar/turbulent interface near the puff's trailing edge, the three-dimensional shear layer above each low-speed streak is intensified and undergoes the Kelvin–Helmholtz instability, which is a peculiar feature, not the case in bypass boundary-layer transition where streak breakdown is caused by the growth of sinuous instability modes. New vortices generated on the interface penetrate into the puff and enhance its turbulent activity.Although this paper has not yet solved the question of the critical Reynolds number, the results make a valuable contribution to understanding of the transition mechanism of pipe flow as well as the dynamics of wall turbulence.