Unstable periodic motion in turbulent flows

G. Kawahara (1) , S. Kida (2) , L. van Veen (3)

1 Department of Mechanical Science
2 Department of Mechanical Engineering and Science
3 Department of Mathematical and Statistical Science

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_?=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.

Domaines: Cosmologie et astrophysique extra-galactique [astro-ph.CO]; Astrophysique [astro-ph]; Sciences de la Terre

G. Kawahara, S. Kida, L. van Veen. Unstable periodic motion in turbulent flows. Nonlinear Processes in Geophysics, 2006, 13 (5), pp.499-507. ⟨hal-00302781⟩