Direct and noisy transitions in a model shear flow

TL;DR

This paper investigates the phase space structure of a simplified 2D shear flow model, analyzing optimal perturbations for different criteria and their scaling with Reynolds number, to better understand transition to turbulence.

Contribution

It introduces a comparative analysis of optimal perturbations based on energy, dissipation, and noise amplitude in a simplified shear flow model.

Findings

Different optimal states trigger transition depending on the criterion.

All optimal states exhibit similar scaling with Reynolds number.

The study highlights the importance of perturbation choice in transition analysis.

Abstract

The transition to turbulence in flows where the laminar profile is linearly stable requires perturbations of finite amplitude. "Optimal" perturbations are distinguished as extrema of certain functionals, and different functionals give different optima. We here discuss the phase space structure of a 2-d simplified model of the transition to turbulence and discuss optimal perturbations with respect to three criteria: energy of the initial condition, energy dissipation of the initial condition and amplitude of noise in a stochastic transition. We find that the states that trigger the transition are different in the three cases, but show the same scaling with Reynolds number.