Modeling the transition to turbulence in shear flows

Abstract

One-dimensional models are presented for transitional shear flows. The models have two variables corresponding to turbulence intensity and mean shear. These variables evolve according to simple equations based on known properties of transitional turbulence. The first model considered is for pipe flow. A previous study modeled turbulence using a chaotic tent map. In the present work turbulence is modeled instead as multiplicative noise. This model captures the character of transitional pipe flow and contains metastable puffs, puff splitting, and slugs. These ideas are extended to a limited model of plane Couette flow.

ETC13 Conference Proceeding, 8 pages, 6 figures

References in corpus (4)

• Computational Study of Turbulent-Laminar Patterns in Couette Flow
• Simplifying the complexity of pipe flow
• Reply to Comment on 'Critical behaviour in the relaminarization of localized turbulence in pipe flow'
• Lifetime statistics in transitional pipe flow

Cited by in corpus (9)

• The rise of fully turbulent flow
• On using Extreme Values to detect global stability thresholds in multi-stable systems: The case of transitional plane Couette flow
• Turbulent patterns in wall-bounded flows: a Turing instability?
• Linear instability of turbulent channel flow
• Semi-analytical approach to criteria for ignition of excitation waves
• Phase transition to turbulence via moving fronts
• Laminar-turbulent patterning in wall-bounded shear flows: a Galerkin model
• Formation of spanwise vorticity in oblique turbulent bands of transitional plane Couette flow, part 2: modelling and stability analysis
• Turbulent spot growth in plane Couette flow: statistical study and formation of spanwise vorticity