Optimal perturbations and transition energy thresholds in boundary layer shear flows

TL;DR

This paper uses adjoint-based optimization to identify minimal energy perturbations that trigger transition to turbulence in boundary layer flows, revealing efficient pathways and thresholds for subcritical transition.

Contribution

It introduces a method to compute the minimal seed in boundary layers and demonstrates the effectiveness of dynamic rescaling in approaching the edge trajectory.

Findings

Identified the critical energy threshold for transition.

Computed the fully localized optimal perturbation (minimal seed).

Showed that dynamic rescaling improves edge trajectory convergence.

Abstract

Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations. In this work, we employ adjoint-based optimization to identify optimal initial perturbations in the Blasius boundary layer, culminating in the computation of the subcritical transition critical energy threshold and the associated fully localized critical optimum in a spatially extended configuration, the so called minimal seed. By dynamically rescaling the variables with the local boundary layer thickness, we show that the identified edge trajectory approaches the same attracting phase space region as previously reported edge trajectories, and reaches the region more efficiently.