Modeling the transition to turbulence in shear flows

TL;DR

This paper introduces simplified one-dimensional models for transitional shear flows, capturing key phenomena like metastable puffs and slugs, and extends these models from pipe flow to plane Couette flow.

Contribution

It presents novel one-dimensional models based on turbulence intensity and mean shear, incorporating multiplicative noise to accurately simulate transitional flow phenomena.

Findings

Models reproduce metastable puffs and slugs in pipe flow

Turbulence modeled as multiplicative noise captures flow dynamics

Extensions to plane Couette flow demonstrate model versatility

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.