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The Diffusion of Passive Tracers in Laminar Shear Flow
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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.
Physical Review Letters
|September 22, 2025
Summary
Body forces can cause discontinuous transitions in pipe flow, deviating from the standard continuous model. A minimal Landau theory reveals a tricritical point explaining these phenomena and heterogeneous states in curved pipes.
Area of Science:
- Fluid dynamics
- Non-equilibrium phase transitions
- Universality classes
Background:
- Laminar-turbulent transition in straight pipes aligns with directed percolation universality.
- Curved pipes or body forces introduce complex phenomenology, including discontinuous transitions.
- Existing models struggle to explain these deviations from the consensus.
Purpose of the Study:
- To investigate the impact of body forces on laminar-turbulent transition in pipes.
- To develop a theoretical framework explaining discontinuous transitions and heterogeneous states.
- To reconcile experimental and simulation observations with theoretical models.
Main Methods:
- Incorporation of body forces into a minimal Landau theory.
- Calculation of the phase diagram based on Reynolds number and body force strength.
- Analysis of tricritical points and spatially heterogeneous states.
Main Results:
- A tricritical point emerges above a critical body force strength.
- This tricritical point explains discontinuous transition behavior.
- The theory accounts for observed spatially heterogeneous flow states.
Conclusions:
- Body forces significantly alter the nature of the laminar-turbulent transition.
- The minimal Landau theory with a tricritical point successfully explains observed phenomena.
- Results align with experimental data from centrifugal pipes and direct numerical simulations.
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