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www.nonlin-processes-geophys.net/13/499/2006/
doi:10.5194/npg-13-499-2006
© Author(s) 2006. This work is licensed
under a Creative Commons License.
Unstable periodic motion in turbulent flows
1Department of Mechanical Science, Graduate School of Engineering Science, Osaka University, Osaka 560-8531, Japan
2Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan
3Department of Mathematical and Statistical Science, La Trobe University, Victoria 3086, Australia
Abstract. 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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Citation: Kawahara, G., Kida, S., and van Veen, L.: Unstable periodic motion in turbulent flows, Nonlin. Processes Geophys., 13, 499-507, doi:10.5194/npg-13-499-2006, 2006. Bibtex EndNote Reference Manager XML
