Approximate streamsurfaces for flow visualization

TL;DR

This paper introduces a method to approximate first integrals from velocity data to better visualize vortical features in 3D flows using streamsurfaces, addressing challenges in flow visualization and identifying key transport barriers.

Contribution

The paper presents a novel approach to construct approximate first integrals from velocity data, enhancing flow visualization and vortex identification in complex 3D flows.

Findings

The method effectively visualizes vortical structures in known flow examples.

It identifies key barriers to momentum transport in turbulent flows.

The approach improves upon existing vortex visualization techniques.

Abstract

Instantaneous features of three-dimensional velocity fields are most directly visualized via streamsurfaces. It is generally unclear, however, which streamsurfaces one should pick for this purpose, given that infinitely many such surfaces pass through each point of the flow domain. Exceptions to this rule are vector fields with a nondegenerate first integral whose level surfaces globally define a continuous, one-parameter family of streamsurfaces. While generic vector fields have no first integrals, their vortical regions may admit local first integrals over a discrete set of streamtubes, as Hamiltonian systems are known to do over Cantor sets of invariant tori. Here we introduce a method to construct such first integrals approximately from velocity data, and show that their level sets indeed frame vortical features of the velocity field in examples in which those features are known from Lagrangian analysis. Moreover, we test our method in numerical data sets, including a flow inside a V-junction and a turbulent channel flow. For the latter, we propound an algorithm to pin down the most salient barriers to momentum transport up to a given scale providing a way out of the occlusion conundrum that typically accompanies other vortex visualization methods.