Equilibrium and travelling-wave solutions of plane Couette flow. (English) Zbl 1183.76688
Summary: We present 10 new equilibrium solutions to plane Couette flow in small periodic cells at low Reynolds number \(Re\) and two new travelling-wave solutions. The solutions are continued under changes of \(Re\) and spanwise period. We provide a partial classification of the isotropy groups of plane Couette flow and show which kinds of solutions are allowed by each isotropy group. We find two complementary visualizations particularly revealing. Suitably chosen sections of their three-dimensional physical space velocity fields are helpful in developing physical intuition about coherent structures observed in low-\(Re\) turbulence. Projections of these solutions and their unstable manifolds from their \(\infty \)-dimensional state space on to suitably chosen two- or three-dimensional subspaces reveal their interrelations and the role they play in organizing turbulence in wall-bounded shear flows.
MSC:
| 76D33 | Waves for incompressible viscous fluids |
Software:
channelflowReferences:
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