Criteria of tracking vortex surfaces in turbulent-like flows

Zishuo Han,Yue Yang

doi:10.1186/s42774-021-00100-y

Abstract

We propose criteria of tracking vortex surfaces in complex flows based on the vortex-surface field (VSF). The criteria characterize the accuracy and Lagrangian tracking performance of the numerical VSF solution, and determine the time period when the vortex surface tracking is satisfactory. Moreover, we develop a turbulent-like flow combining large-scale coherent structures in the Taylor–Green flow and small-scale turbulent structures in homogeneous isotropic turbulence (HIT). From tracking of vortex surfaces during the effective tracking period, we find that the imposed HIT disturbance significantly wrinkles vortex surfaces. Subsequently, the wrinkled vortex tube with large vorticity magnitude tends to be further twisted, contributing to energy cascade, while the wrinkling is mitigated in the region with small vorticity magnitude.

Highlights

The vortex-surface field (VSF) is a Lagrangian-based method to identify and characterize coherent vortical structures [1, 2]
The VSF reveals the continuous rolling-up and twisting of vortex tubes in Taylor–Green (TG) flows [6], and the complex network of tangling vortex tubes in homogeneous isotropic turbulence (HIT) [5], instead of the visual “breakdown” of worm-like structures identified by Eulerian vortex criteria [9, 10]
We address the issue on the comprehensive assessment of vortex surface tracking by proposing new criteria in the VSF calculation, and develop a turbulent-like flow combing the large-scale coherent structures and small-scale turbulent structures to assess VSF solutions with moderate computational resources

Summary

Introduction

The vortex-surface field (VSF) is a Lagrangian-based method to identify and characterize coherent vortical structures [1, 2]. The challenges of tracking vortex surfaces in turbulent-like complex flows are rooted in the breakdown of the Helmholtz theorem in real flows, which can cause the non-existence and non-uniqueness of VSF solutions. The former issue has been partially resolved using the two-time method.

Simulation overview

Criteria of VSF tracking

Evolution of VSFs

Findings

Conclusions