On Constructing the Minimal Seed of Turbulence: Nonlinear Transient Growth

TL;DR

This paper shows that incorporating nonlinearity into transient growth analysis reveals more effective localized 3D disturbances for triggering turbulence in pipe flow, surpassing linear predictions.

Contribution

It introduces a nonlinear optimal disturbance framework that better predicts efficient turbulence triggers in shear flows compared to traditional linear methods.

Findings

Nonlinear analysis predicts localized 3D disturbances as optimal.

Nonlinear optimal disturbances are more effective in triggering turbulence.

Linear and nonlinear predictions differ significantly in shear flow transition.

Abstract

Linear transient growth analysis is commonly used to suggest the structure of disturbances which are particularly efficient in triggering transition to turbulence in shear flows. We demonstrate that the addition of nonlinearity to the analysis can substantially change the prediction made in pipe flow from simple 2 dimensional streamwise rolls to a spanwise and cross-stream localised 3 dimensional state. This new nonlinear optimal is demonstrably more efficient in triggering turbulence than the linear optimal indicating that there are better ways to design perturbations to achieve transition.