Phase Transition to Turbulence via Moving Fronts

Area of Science:

• Fluid dynamics
• Turbulence
• Phase transitions

Background:

• Directed percolation (DP) is a universality class for continuous phase transitions.
• DP has been linked to turbulence in subcritical wall-bounded flows.
• Canonical flows exhibit discrete turbulent structures (puffs/bands) that self-replicate or laminarize.

Purpose of the Study:

• To investigate the universality of turbulence transition in subcritical shear flows.
• To explore transition mechanisms beyond discrete structures in plane Couette flow.
• To map the observed transition onto a stochastic system.

Main Methods:

• Numerical experiment designed to eliminate discrete turbulent structures in plane Couette flow.
• Analysis of turbulence proliferation via expanding fronts and decay via laminar zone creation.
• Mapping the phase transition to a stochastic one-variable system.

Main Results:

• Plane Couette flow exhibits a simpler transition scenario than canonical flows, without discrete structures.
• Turbulence proliferates through expanding fronts and decays via spontaneous laminar zone formation.
• The transition's nature (discontinuous or DP-class continuous) depends on turbulent fluctuation levels.

Conclusions:

• The transition mechanism in plane Couette flow differs from canonical pipe and planar flows.
• This finding challenges the universality of discrete structure-mediated turbulence transition.
• The results have significant implications for understanding turbulence in various hydrodynamic systems.