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Updated: Jan 17, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Tricritical Directed Percolation Controls the Laminar-Turbulent Transition in Pipes with Body Forces
Guru K Jayasingh1, Nigel Goldenfeld1
1University of California, Department of Physics, San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA.
Abstract:
The laminar-turbulent transition in straight pipes is believed to occur through a continuous nonequilibrium phase transition in the directed percolation universality class. However, in curved pipes or in the presence of body forces it is possible to observe a discontinuous transition and other phenomenology which seem inconsistent with the emerging consensus. Here, we consider the perturbing effects of body forces and incorporate them into a minimal Landau theory of the transition. We calculate the phase diagram as a function of Reynolds number and body force strength, and show that above a threshold strength of the latter, there is a tricritical point which accounts for the observed discontinuity behavior, including spatially heterogeneous states. Our results are consistent with recent experiments in centrifugal pipes and direct numerical simulations of heated flows.
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