Stochastic Model for Quasi-One-Dimensional Transitional Turbulence with Streamwise Shear Interactions

The transition to turbulence in wall-bounded shear flows is typically subcritical, with a poorly understood interplay between spatial fluctuations, pattern formation, and stochasticity near the critical Reynolds number. Here, we present a spatially extended stochastic minimal model for the energy budget in transitional pipe flow, which successfully recapitulates the way localized patches of turbulence (puffs) decay, split, and grow, respectively, as the Reynolds number increases through the laminar-turbulent transition. Our approach takes into account the flow geometry, as we demonstrate by extending the model to quasi-one-dimensional Taylor-Couette flow, reproducing the observed directed percolation pattern of turbulent patches in space and time.

Automated summary

In this study, a spatially extended stochastic minimal model is proposed to describe the energy budget in transitional flows, taking into account the influence of flow geometry. The model successfully replicates the decay, splitting, and growth processes of localized turbulent patches in transitional flows as the Reynolds number increases. The model is also extended to quasi-one-dimensional Taylor-Couette flow, reproducing the directed percolation pattern observed in space and time.