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A note on the mirror-symmetric coherent structure in plane Couette flow. (English) Zbl 1291.76133
Summary: We note that the mirror-symmetric solution in plane Couette flow, found recently by J. F. Gibson, J. Halcrow and P. Cvitanović [J. Fluid Mech. 611, 107–130 (2008; Zbl 1151.76453)] and T. Itano and S. C. Generalis [Phys. Rev. Lett. 102, No. 114501 (2009)], belongs to the solution group classified as ‘ribbon’ in rotating-plane Couette flow (RPCF). It represents a subcritical (in terms of the system rotation) solution at zero rotation rate on the three-dimensional tertiary flow branch which bifurcates from the second streamwise-independent flow in RPCF. The way of its appearance is similar to that of the Nagata solution [M. Nagata, J. Fluid Mech. 217, 519–527 (1990)], which lies on the subcritical three-dimensional tertiary flow branch bifurcating from the first streamwise-independent flow in RPCF.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76E30 Nonlinear effects in hydrodynamic stability
76F06 Transition to turbulence
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