Exact solutions: Periodic orbits

Equilibria are steady states of the Navier-Stokes flow. As -by definition- they do not move, they cannot be “turbulent.” Turbulent dynamics is captured by the (infinity of) unstable periodic solutions, 3D movies that repeat exactly after some finite time T.

The next three movies show three of the new periodic orbits computed by our group (viewing one will suffice to get the idea):

T=  75.348     (1 MB) Computations were performed with Viswanath's Newton - hookstep - GMRES search algorithm from close recurrences in a single u(x,t) trajectory.

Each orbit lies within the S-invariant subspace of HKW cell and is a true periodic orbit (no x or z translation after a completed period).
T=  88.905    (1.5 MB)
T=  99.70     (1.3 MB)

The first orbits of this type within the S-invariant subspace were computed by Kawahara & Kida, while the first “relative periodic” orbits in the full state-space of plane Couette were computed by Viswanath.

click here for more solutions in the database