Kawahara, Genta; Kida, Shigeo Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst. (English) Zbl 0996.76034 J. Fluid Mech. 449, 291-300 (2001). Summary: Two time-periodic solutions with genuine three-dimensional structure are numerically discovered for incompressible Navier-Stokes equation of a constrained plane Couette flow. One solution with strong variation in spatial and temporal structure exhibits a full regeneration cycle, which consists of the formation and breakdown of streamwise vortices and low-velocity streaks; the other one, of gentle variation, represents a spanwise standing-wave motion of low-velocity streaks. These two solutions are unstable, and the corresponding periodic orbits in the phase space are connected with each other. A turbulent state wanders around the strong one for most of the time except for occasional escapes from it. As a result, the mean velocity profile and the root-mean-squares of velocity fluctuations of the plane Couette turbulence agree very well with the temporal averages of those of this periodic motion. After an occasional escape from the strong solution, the turbulent state reaches the gentle periodic solution and returns. On the way back, it experiences an overshoot accompanied by strong turbulence activity like an intermittent bursting phenomenon. Cited in 2 ReviewsCited in 81 Documents MSC: 76F10 Shear flows and turbulence 76D05 Navier-Stokes equations for incompressible viscous fluids 76M22 Spectral methods applied to problems in fluid mechanics Keywords:incompressible Navier-Stokes equation; constrained plane Couette flow; regeneration cycle; mean velocity profile; strong turbulence; intermittent bursting phenomenon PDF BibTeX XML Cite \textit{G. Kawahara} and \textit{S. Kida}, J. Fluid Mech. 449, 291--300 (2001; Zbl 0996.76034) Full Text: DOI