arXiv subjects

Zishuo Han

Publications and source records attributed to Zishuo Han.

2 recordsLinked to original sources

arXiv2025

Modelling and synthesizing turbulence with multi-scale coherent vortices

Turbulence is a complex system exhibiting both universal statistical features and prominent coherent structures. We model turbulence using coherent vortices distributed within a multi-scale statistical framework, termed `woven turbulence'. These entangled vortices are generated based on fractional Brownian bridges, with scale-dependent parameters set by dimensional analysis and geometric similarity. By integrating statistical and structural modeling, our approach naturally captures both the universal statistical features of turbulence and its coherent vortex structures. The spatial filling fraction of vortices in woven turbulence, termed `vortex density', is tunable, enabling us to investigate the statistical-structural interaction and uncover two concise physical insights of turbulence. First, the invariance of the hierarchical vortex density across scales corresponds to Kolmogorov's $-5/3$ law in the inertial range. Second, there exists a critical total vortex density at which the intermittency of woven turbulence closely matches that of real turbulence, and this critical density converges to a finite value in the inviscid limit. Deviating from this critical density reveals a negative correlation between intermittency and total vortex density. In addition, woven turbulence also serves as a fast turbulence synthesis method, requiring only the Taylor-Reynolds number as input and exhibiting an extremely low computational cost proportional to the grid size. It generates instantaneous turbulent fields at Taylor-Reynolds numbers of order $10^3$ on $4096^3$ grid points, with computational cost over five orders of magnitude lower than that of direct numerical simulation.

physics.flu-dyn↗

arXiv2025

Constructing wall turbulence using hierarchical hairpin vortices

Wall-bounded turbulence is characterized by coherent, worm-like structures such as hairpin vortices. The attached-eddy model provides a successful statistical framework for the log-law region, yet the complex geometry and multiscale nature of wall-turbulence vortices remain challenging for physics-based modelling. Here, we model wall turbulence as an ensemble of complex vortices, introducing a systematic approach to constructing turbulence fields enriched with hierarchically organized hairpin vortex packets. The geometry and organization of the vortex packets are calibrated to match observations, enabling the model to reproduce both attached and detached motions through a height-dependent core-size variation. Our model successfully reproduces the key statistical and structural features of wall turbulence, matching direct numerical simulations of turbulent channel flow at friction Reynolds numbers from 1,000 to 10,000. More importantly, it also reveals new insights into the coherent structures, emphasizing the role of vortex geometry, packet organization, and hierarchy in setting the attached/detached balance, meandering streaks and inclination angles, superstructure alignment, and the overall partition of contributions. Moreover, the constructed channel turbulence rapidly transitions into fully developed turbulence in direct numerical simulation, demonstrating its physical self-consistency and practical utility for initializing high-fidelity simulations. This approach significantly reduces computational costs associated with turbulence development while providing a flexible framework for testing and advancing turbulence models based on vortex structures.

physics.flu-dyn↗