Geometrical statistics and vortex structures in helical and nonhelical turbulences

Abstract

In this paper we conduct an analysis of the geometrical and vortical statistics in the small scales of helical and non-helical turbulence generated with direct numerical simulations. Using a filtering approach, the helicity flux from large scales to small scales is represented by the subgrid-scale (SGS) helicity dissipation. The SGS helicity dissipation is proportional to the product between the SGS stress tensor and the symmetric part of the filtered vorticity gradient, a tensor we refer to as the vorticity strain rate. We document the statistics of the vorticity strain rate, the vorticity gradient, and the dual vector corresponding to the anti-symmetric part of the vorticity gradient. These results provide new insights into the local structures of the vorticity field. We also study the relations between these quantities and vorticity, SGS helicity dissipation, SGS stress tensor, and other quantities. We observe that in both helical and non-helical turbulence: (1) there is a high probability to find the dual vector aligned with the intermediate eigenvector of the vorticity strain rate tensor; (2) vorticity tends to make an angle of 45 degrees with both the most contractive and the most extensive eigen-directions of the vorticity strain rate tensor; (3) the vorticity strain rate shows a preferred alignment configuration with the SGS stress tensor; (4) in regions with strong straining of the vortex lines, there is a negative correlation between the third order invariant of the vorticity gradient tensor and SGS helicity dissipation fluctuations. The correlation is qualitatively explained in terms of the self-induced motions of local vortex structures, which tend to wind up the vortex lines and generate SGS helicity dissipation. In helical turbulence, we observe that the joint probability density function of the second and third tensor invariants of the vorticity gradient displays skewed distributions, with the direction of skewness depending on the sign of helicity input. We also observe that the intermediate eigenvalue of the vorticity strain rate tensor is more probable to take negative values. These interesting observations, reported for the first time, call for further studies into their dynamical origins and implications.

Spatial evolution of the helical behavior and the 2/3 power-law in single-square-grid-generated turbulence

“…However, there are also experimental (Wallace et al 1992 on turbulent boundary layer, two-stream turbulent mixing layer, and turbulent grid flow) and numerical (Rogers and Moin 1987 on homogeneous turbulence and turbulent channel flow) studies that do not support this argument. Recently, Li (2010) used a filtering approach to study the helicity cascade and presented a geometrical analysis of both helical and nonhelical turbulences. Li (2010) identified some features which are unique in helical turbulence.…”

Helical Turbulence in Fluids and MHD

“…Other helical models have been devised recently [21][22][23][24]. For example, in [23], it is shown by assuming a Kolmogorov spectrum valid in the absence of rotation that the classical Smagorinsky model underestimates energy and helicity dissipation by 40 %, although numerically the effect seems smaller.…”

“…Unsurprisingly, the helicity spectrum is much better described when using this helical subgrid scale model [22]; but one can remark that the growth rate of the total energy in the inverse cascade in rotating flows is also better estimated using this helical model. Finally, it has also been found that sub-grid helicity dissipation is responsible for observed asymmetries in the joint Probability Distribution Functions of the invariants of the vorticity gradient tensor, an asymmetry attributed to the geometry of twisted vortex tubes [24].…”

Dynamic Phase Alignment in Navier-Stokes Turbulence

“…While we provided significant evidence for the existence and importance of dynamic phase alignment, we stopped short of characterizing how it emerges from the nonlinear interactions. Dynamic phase alignment need not be regarded as necessarily alternative to other proposed paradigms for characterizing imbalanced turbulence [6,7,19,38,[46][47][48][49][50][51]. As an example, Ref.…”