Vortex axis three-dimensional bidirectional reconstruction method

Vortices play a critical role in the generation and sustenance of turbulence, making their accurate identification essential for elucidating flow mechanisms, addressing turbulence-related challenges, and enabling flow control. While existing VATIP algorithms reconstruct individual vortex topologies, they exhibit notable deficiencies in three-dimensional sampling and erroneous connection suppression. To address this, we propose a novel algorithm: Vortex Axis Three-Dimensional Bidirectional Reconstruction (VATBR). By leveraging the vectorial properties of Liutex, VATBR introduces two key enhancements: (1) multi-directional (three spatial axes) initialisation of vortex axis matching, substantially improving reconstruction of complex three-vortex structures; and (2) physical constraints via Liutex direction, replacing the ‘nearest point criterion’ with a ‘nearest predicted point criterion’ to minimise erroneous inter-vortex connections. Validation in an idealised perturbed flow field demonstrates VATBR's superior three-dimensional sampling under identical conditions. Quantitative error analysis shows that VATBR yields markedly lower average distance error and average angle error than VATIP, indicating that the Liutex-direction-based physical constraint effectively suppresses erroneous inter-vortex connections. Applied to direct numerical simulation (DNS) data of open-channel flow (OCF) and closed-channel flow (CCF) at friction Reynolds numbers (Reτ) of 300, 500, and 700, VATBR successfully extracted diverse vortex structures. Statistical analysis shows that, with increasing Reτ, the proportion of streamwise vortices decreases while three-dimensional vortices rise in both flows; streamwise and spanwise mean vortex scales diminish, yet the spanwise-to-streamwise scale ratio increases, indicating enhanced vortex bending and folding at higher Reτ. Joint probability density distributions of vortex head/tail wall-normal positions reveal markedly lower near-surface densities for three-dimensional vortices in OCF versus CCF, attributable to free-surface-induced vertical suppression. VATBR effectively overcomes VATIP's primary limitations, delivering precise and reliable three-dimensional vortex topology reconstructions. This algorithm provides a robust tool for statistical and dynamical analyses of near-wall turbulent structures, advancing mechanistic understanding and informing flow control strategies.