Stuff on periodic orbits to appear here!
Periodic orbits in pipe flow
Pipe flow, Re=2500. Regions of flow, slower than the mean flow is indicated in blue, called 'streaks'. Rotating 'vortex structures' are indicated in yellow. To simplify analysis a 4-fold rotational symmetry has been imposed. This does not significantly affect statistical properties of the flow, e.g. the turbulent friction factor:
Viewed in a moving frame, recurring patterns are observed - periodic orbits:
A spatially localised patch of turbulence:
Periodic orbits in pipe flow, visualised in terms of their input (I), dissipation (D) and kinetic energy (E), relative to their laminar values: