Edge state modulation by mean viscosity gradients

TL;DR

This study investigates how spatially non-uniform viscosity affects edge states in channel flows, revealing that viscosity gradients can modulate transition thresholds by altering the energy and stability of these states.

Contribution

It provides a non-linear theoretical framework supported by simulations to explain how viscosity gradients influence edge state energy, stability, and transition thresholds in shear flows.

Findings

Decreasing viscosity away from walls weakens edge state structures.

Viscosity gradients shift the edge state's position in state space.

Transition thresholds are modulated by the direction and magnitude of viscosity gradients.

Abstract

Motivated by the relevance of edge state solutions as mediators of transition, we use direct numerical simulations to study the effect of spatially non-uniform viscosity on their energy and stability in minimal channel flows. What we seek is a theoretical support rooted in a fully non-linear framework that explains the modified threshold for transition to turbulence in flows with temperature-dependent viscosity. Consistently over a range of subcritical Reynolds numbers, we find that decreasing viscosity away from the walls weakens the streamwise streaks and the vortical structures responsible for their regeneration. The entire self-sustained cycle of the edge state is maintained on a lower kinetic energy level with a smaller driving force, compared to a flow with constant viscosity. Increasing viscosity away from the walls has the opposite effect. In both cases, the effect is proportional to the strength of the viscosity gradient. The results presented highlight a local shift in the state space of the position of the edge state relative to the laminar attractor with the consequent modulation of its basin of attraction in the proximity of the edge state and of the surrounding manifold. The implication is that the threshold for transition is reduced for perturbations evolving in the neighbourhood of the edge state in case viscosity decreases away from the walls, and vice versa.