Line segments in homogeneous scalar turbulence

Abstract

The local structure of a turbulent scalar field in homogeneous isotropic turbulence is analyzed by direct numerical simulations (DNS) with different Taylor micro-scale based Reynolds numbers between 119 and 529. A novel signal decomposition approach is introduced where the signal of the scalar along a straight line is partitioned into segments based on the local extremal points of the scalar field. These segments are then parameterized by the distance ℓ between adjacent extremal points and the scalar difference Δϕ at the extrema. Both variables are statistical quantities and a joint distribution function of these quantities contains most information to statistically describe the scalar field. It is highlighted that the marginal distribution function of the length becomes independent of Reynolds number when normalized by the mean length ℓm. From a statistical approach, it is further shown that the mean length scales with the Kolmogorov length, which is also confirmed by DNS. For turbulent mixing, the scalar gradient plays a paramount role. Turbulent scalar fields are characterized by cliff-ramp-like structures manifesting the occurrence of localized large scalar gradients. To study turbulent mixing, a segment-based gradient is defined as Δϕ/ℓ. Joint statistics of the length and the segment-based gradient provide novel understanding of cliff-ramp-like structures. Ramp-like structures are unveiled by the asymmetry of the joint distribution function of the segment-based gradient and the length. Cliff-like structures are further analyzed by conditional statistics and it is shown from DNS that the width of cliffs scales with the Kolmogorov length scale.