Transient turbulence: a narrative
[keep the movie from the previous slide running in a separate window]
The state-space trajectory is plotted against three exact equilibria of plane Couette flow:
the lower-branch (LB, blue)
the upper-branch (UB, green)
the "newbie" (NB, red)plus the laminar solution (LM, black) (see equilibria). The half-cell translations in x and z of the equilibria are points indicated with prefix
"τx", "τz", and "τxz".
The blue and green solid lines show the 1 and 2-dimensional unstable manifolds of the LB and UB equilibria. The moving red dot is the state of the fluid velocity field evolving under the Navier-Stokes equations. |
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