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Formation of turbulent patterns near the onset of transition in plane Couette flow. (English) Zbl 1189.76254
Summary: The formation of turbulent patterns in plane Couette flow is investigated near the onset of transition, using numerical simulation in a very large domain of size \(800 h \times 2 h \times 356 h\). Based on a maximum observation time of 20 000 inertial units, the threshold for the appearance of sustained turbulent motion is \(Re_{c} = 324 \pm 1\). For \(Re_{c} < Re \leqslant 380\), turbulent-banded patterns form, irrespective of whether the initial perturbation is a noise or localized disturbance. Measurements of the turbulent fraction versus Re show evidence for a discontinuous phase transition scenario where turbulent spots play the role of the nuclei. Using a smaller computational box, the angle selection of the turbulent bands in the early stages of their development is shown to be related to the amplitude of the initial perturbation.

MSC:
76F06 Transition to turbulence
76F65 Direct numerical and large eddy simulation of turbulence
Software:
SIMSON
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