乱流に埋め込まれた不安定周期運動(<小特集>乱流研究の最前線)

概要

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Recently found unstable time-periodic solutions to the incompressible Navier-Stokes equation are reviewed to discuss their relevance to plane Couette turbulence and isotropic turbulence. It is shown that the periodic motion embedded in the Couette turbulence exhibits a regeneration cycle of near-wall coherent structures, which consists of formation and breakdown of streamwise vortices and low-velocity streaks. In phase space a turbulent state wanders around the corresponding periodic orbit for most of the time, so that the root-mean-squares of velocity fluctuations of the Couette turbulence agree very well with the temporal averages of those along the periodic orbit. The Kolmogorov universal-range energy spectrum is observed for the periodic motion embedded in high-symmetric turbulence at the Taylor-microscale Reynolds number Re_λ=67. A laminarization strategy inspired by investigation of the phase-space structure in the vicinity of the unstable periodic orbit is presented for a drag reduction of the Couette turbulence. The periodic orbit to be used for laminarization is on the separatrix between the basin of attraction of turbulent and laminar flows. During natural or forced approaches of the turbulent state to the periodic orbit weak spanwise rotation is imposed on the fluid so that the state can go beyond the separatrix toward the laminar flow.
2006-12-25