How does turbulence break into stripes in a channel flow?
As a channel flow slows toward laminar, turbulence organizes into tilted stripes whose angle stays near 25 degrees before the pattern breaks up, while the friction coefficient stays roughly constant.
Source
Flow Statistics in the Transitional Regime of Plane Channel Flow
Study at a glance
- Design
- Computational / modelling — Direct numerical simulation of pressure-driven plane channel flow in large periodic domains, lowering the friction Reynolds number step by step from 100 to 39.
- N
- No participant N; simulations at a series of friction Reynolds numbers between 39 and 100.
- Population
- Simulated incompressible flow between two parallel plates (plane Poiseuille flow)
- Outcome
- Turbulent band angle, laminar gap size distribution, friction factor, and moments of local Reynolds numbers and cross-flow energy
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What they did
The authors simulated fluid driven by a pressure gradient between two flat plates, using very large periodic computational boxes so many turbulent structures could coexist. Starting from fully turbulent flow they reduced the driving (the friction Reynolds number) in small steps and let the flow settle at each level. They measured the tilt of turbulent bands two independent ways, the sizes of laminar gaps between bands, the friction factor, and the full statistical distributions of local Reynolds numbers and turbulent energy.
What they found
Uniform turbulence gave way to oblique stripes with competing orientations, then to isolated parallel bands at the lowest flow rates. In the stripe regime the band angle was nearly constant at about 25 degrees, rising toward 40 degrees as the pattern fragmented, and the friction factor stayed near 0.01. Laminar gap sizes had exponential rather than power-law tails at every flow rate studied, so the whole range is intermittent but not critical. The skewness and kurtosis of wall shear stress and turbulent energy grew as the flow slowed and followed the same kurtosis-versus-skewness-squared relation seen in fully developed turbulence.
The limits
What it doesn't show
The lowest simulated flow rate is still above the estimated critical point, so the study cannot say how the transition itself behaves or which universality class it belongs to; the authors say that would need even bigger domains and longer runs. Results come from periodic boxes, which may impose some constraints compared with a real finite channel. The analogy with first-order phase transitions is suggested, not demonstrated, and the kurtosis-skewness relation is observed without an explanation.
Key terms
- Reynolds number
- A dimensionless ratio of inertial to viscous effects; low values give smooth laminar flow, high values give turbulence.
- Plane Poiseuille flow
- Flow between two fixed parallel plates driven by a constant pressure gradient; its laminar profile is a parabola.
- Spatio-temporal intermittency
- A state where laminar and turbulent regions coexist and shift in both space and time.
- Friction factor
- A dimensionless measure of wall drag relative to the flow's kinetic energy, plotted against Reynolds number in the Moody diagram.
- Kurtosis and skewness
- Third and fourth standardized moments of a distribution that measure its asymmetry and the heaviness of its tails.
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Quiz yourself
What distinguishes spatio-temporal intermittency from a critical point in this study?
Common questions
Why does the exponential gap distribution matter?
At a critical point, gap sizes would show power-law tails from scale invariance; exponential tails mean the system is still some distance from the actual transition threshold.
Why were such large simulation domains needed?
The stripes are very long and widely spaced, so small boxes force artificial arrangements and hide features like the constant friction factor.
What is the phase-transition analogy?
Laminar and turbulent regions coexist like two phases, and a constant friction factor resembles a quantity held fixed during phase coexistence, but the authors treat this as an idea to develop.
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