Objective Momentum Barriers in Wall Turbulence

TL;DR

This paper introduces a frame-indifferent method to identify internal momentum transport barriers in wall turbulence, revealing features that better block diffusive momentum flux than traditional vortex-based approaches.

Contribution

It develops a novel, frame-indifferent approach using invariant manifolds and Lagrangian diagnostics to identify and analyze momentum transport barriers in wall turbulence.

Findings

MTBs outperform classic vortices in blocking momentum flux

Elliptic manifold approximations effectively identify coherent structures

Normalized trajectory metrics enable unbiased visualization of turbulence features

Abstract

We use the recent frame-indifferent theory of diffusive momentum transport to identify internal barriers in wall-bounded turbulence. Formed by the invariant manifolds of the Laplacian of the velocity field, the barriers block the viscous part of the instantaneous momentum flux in the flow. We employ the level sets of single-trajectory Lagrangian diagnostic tools, the trajectory rotation average and trajectory stretching exponent, to approximate both vortical and internal wall-parallel momentum transport barrier (MTB) interfaces. These interfaces provide frame-indifferent alternatives to classic velocity-gradient-based vortices and high-shear boundaries between uniform momentum zones (UMZs). Indeed, we find that these elliptic manifold approximations and MTBs outperform standard vortices and UMZ interfaces in blocking diffusive momentum transport, suggesting our momentum barriers are physical features that may be the cause of coherence signatures in statistical and non-objective diagnostics. We also introduce normalized trajectory metrics that provide unprecedented visualizations of objective coherent structures by avoiding strong turbulence biases.