Criteria of tracking vortex surfaces in turbulent-like flows

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.