# Geometric nature of particle trajectories

입자의 궤적을 통해 알수있는 곡률(curvature) 및 비틀림률(torsion)의 성질을 조사함으로써, 난류의 회전구조 및 헬리시티와의 상관성을 조사하였다.

The geometric nature of particle trajectory is investigated using direct numerical simulation of isotropic turbulence. Probability density functions and autocorrelations along a fluid particle trajectory associated with geometric quantities such as curvature and torsion of the Lagrangian trajectory are provided. We proposed the ratio of torsion to curvature as parameter to identify the particle trajectory and it is found to play crucial role in understanding the geometric shape of particle trajectory. The relationship between Lagrangian helicity and the ratio of torsion to curvature is investigated where Lagrangian helicity is defined as dot product of velocity and vorticity at the point of fluid particle. We found that probability density functions of torsion and torsion normalized by curvature clearly show well-established slope in log–log plots. Lagrangian helicity is intermittently distributed and high Lagrangian helicity is always found, where high acceleration is observed. Regarding the relationship between coherent structure and acceleration, coherent structure can be understood in terms of Lagrangian helicity, curvature, and torsion. Geometric characteristics for solid particles are also investigated and its results are varied according to Stokes number.

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