Unstable periodic motion in turbulent flows

Kawahara, G.; Kida, S.; van Veen, L.

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 Reλ=67. A laminarization strategy inspired by investigation of the phase-space structure in the vicinity of the unstable periodic orbit is presented for the Couette turbulence.

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Kawahara, G. / Kida, S. / van Veen, L.: Unstable periodic motion in turbulent flows. 2006. Copernicus Publications.

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