Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

Abstract

In a three-dimensional simulation higher-order derivative correlations, including skewness and flatness (or kurtosis) factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. Up to 1283 grid points are used with periodic boundary conditions in all three directions to achieve Rλ to 82.9. The equations are forced to maintain steady-state turbulence and collect statistics. The scalar-derivative flatness is found to increase much faster with Reynolds number than the velocity-derivative flatness, and the velocity- and mixed-derivative skewnesses do not increase with Reynolds number. Separate exponents are found for the various fourth-order velocity-derivative correlations, with the vorticity-flatness exponent the largest. This does not support a major assumption of the lognormal and β models, but is consistent with some aspects of structural models of the small scales. Three-dimensional graphics show strong alignment between the vorticity, rate-of-strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short $-\frac{5}{3}$ spectral regime is observed.

Vortex Stretching as a Mechanism for Quantum Kinetic Energy Decay

“…Could large simulations provide the clues? As in the classical case [6,7], a large simulation of a quantum vortex tangle [8] reproduces many experimental properties, including -5/3 spectra [9,10]. However.…”

Universality and scaling phenomenology of small-scale turbulence in wall-bounded flows

“…Both the largest compressing and stretching components of the rate of strain were oriented perpendicular to the tube, while the weak stretching component (the intermediate eigenvector of the strain rate tensor) was aligned along the tube, that is, there was a preferential alignment of the vorticity vector with the intermediate strain direction. This alignment was further investigated by Ashurst et al 4 using the DNS data of isotropic turbulence 2 and homogeneous shear flow. 5 They confirmed the alignment and argued that it was a consequence of angular momentum conservation.…”

Flow resistance in natural, turbulent channel flows: The need for a fluvial fluid mechanics

“…Because such work requires joint consideration of Q and R, and because the latter has not been investigated in detail for complex, vegetative forcings, it follows that this represents a big unknown in fluvial fluid mechanics research, and without it we cannot link topology and dissipation without postulating some form of similarity to the classical behavior considered in these references. Such work has shown that local dissipation takes place near vortex tubes but is organized into sheet-like structures [Kerr, 1985]. A template model for this phenomenon is the stretched spiral vortex [Lundgren, 1982] shown in Figure 3.…”