Cluster statistics of homogeneous fluid turbulence

The intermittent property is investigated for numerically simulated incompressible three-dimensional fluid turbulence at Taylor microscale Reynolds number ${\mathit{R}}_{\lambda }$∼100, 120, and 180. Cluster statistics applied to energy dissipation and velocity (spatial-) derivative fields characterize several intermittent properties, such as the degrees of concentration and the connectivity of regions of large magnitude. Some power-law behavior with a universal exponent appears in the statistics of the energy-dissipation field. Cluster statistics for the derivative field confirm the well-known experimental result that a higher-order derivative field is more intermittent. Moreover, the longitudinal- and the lateral-derivative velocity fields show some differences in the statistics: The former field has smaller concentration, and its cluster pattern is more spotty than the latter field.