乱流中の不安定周期運動

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 r.m.s. (root-mean-squares) of velocity fluctuations of the Couette turbulence agree very well with the temporal averages of those along the periodic orbit. The maximum values of the streamwise and wall-normal r.m.s. velocities for the periodic solution are compared with those for other known nonlinear solutions. 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.
2005-09-27