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The role of coherent structures in low-Reynolds-number turbulent wall flows

Kawahara, G (Osaka)
Thursday 11 September 2008, 11:30-11:50

Seminar Room 1, Newton Institute


Coherent states found numerically in plane Couette turbulence (Kawahara & Kida, J. Fluid Mech. 449, 2001; Kawahara, Phys. Fluids 17, 2005) and square duct turbulence (Uhlmann, Pinelli, Kawahara & Sekimoto, J. Fluid Mech. 588, 2007) are reviewed to discuss the role of coherent structures in wall-bounded turbulent flows at low Reynolds numbers. The coherent states in Couette flow are represented by unstable periodic solutions to the incompressible Navier-Stokes equation. The periodic solution, which exhibits a near-wall regeneration cycle of streamwise vortices and streaks, is shown to satisfy Prandtl's wall law, implying that the regeneration cycle has relevance to the statistical law of near-wall turbulent flow. The coherent states in marginally turbulent square duct flow are characterized by a four-vortex secondary flow and associated streaks. It is shown that at low Reynolds numbers streamwise vortices play a crucial role in the appearance of secondary flow of Prandtl's second kind.


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