Transition to turbulence in a shear flow

Abstract

We analyze the properties of a 19 dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large Re additional stationary flows occur; they are all unstable. The lifetimes of finite amplitude perturbations show a fractal dependence on amplitude and Reynolds number. These findings are in accord with observations on plane Couette flow and suggest a universality of this transition szenario in shear flows.

revtex, 10 pages, 11 figures (included)

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