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Updated: May 5, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Transition of planar Couette flow at infinite Reynolds numbers
Tomoaki Itano1, Takeshi Akinaga, Sotos C Generalis
1Department of Pure and Applied Physics, Faculty of Engineering Science, Kansai University, Osaka 564-8680, Japan.
Abstract:
An outline of the state space of planar Couette flow at high Reynolds numbers (Re<10^{5}) is investigated via a variety of efficient numerical techniques. It is verified from nonlinear analysis that the lower branch of the hairpin vortex state (HVS) asymptotically approaches the primary (laminar) state with increasing Re. It is also predicted that the lower branch of the HVS at high Re belongs to the stability boundary that initiates a transition to turbulence, and that one of the unstable manifolds of the lower branch of HVS lies on the boundary. These facts suggest HVS may provide a criterion to estimate a minimum perturbation arising transition to turbulent states at the infinite Re limit.
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