A Generic Self-Sustaining Process in Shear Flows
Below is a partial list of papers on the nonlinear Self-Sustaining Process
that appears to be a generic mechanism in shear flows. The mechanism has three main
elements
- Streamwise rolls sustain "streaks" (i.e. spanwise (z) modulation of the streamwise velocity),
by redistributing the mean momentum,
- the streaks breakdown through a wake-like instability due to the
spanwise inflections,
- the streamwise rolls are sustained by the non-linear development
of the streak instability.
One notable omission is: James Hamilton, John Kim and Fabian Waleffe, "Regeneration mechanisms of
near-wall turbulence structures," Journal of Fluid Mechanics 287,
pp. 317-348 (March 1995).
Here is a significant figure (111 Kbytes) from that paper showing that
the breakdown of streaks
reenergizes the streamwise rolls that created the streaks
in the first place. This is for plane Couette flow (i.e. the top wall moves out of the screen
and the bottom wall into it). The left figures are contours of streamwise velocity (i.e.
out of the screen) and those on the right are the velocity vectors for the other two
components. This figure is from a Direct Numerical Simulation.
-
Transition in shear flows: Nonlinear normality versus non-normal linearity (165 Kb)
by Fabian Waleffe.
Physics of Fluids 7, pp. 3060-3066.
-
Hydrodynamic Stability and Turbulence: Beyond transients to a self-sustaining process (241 Kb)
by Fabian Waleffe.
Studies in Applied Mathematics, 95, pp. 319-343 (1995).
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On the Origin of Streaks in Turbulent Shear Flows (383 Kb)
by Fabian Waleffe, John Kim and James Hamilton.
Eds. F. Durst et al., in "Turbulent Shear Flows 8: selected papers from the
Eighth International Symposium on Turbulent Shear Flows, Munich, Germany, Sept. 9-11, 1991."
Springer-Verlag, Berlin, 1993.