Vortex polarization and circulation statistics in isotropic turbulence

We carry out an in-depth analysis of a recently introduced vortex gas model of homogeneous and isotropic turbulence. Direct numerical simulations are used to provide a concrete physical interpretation of one of the model's constituent fields: the degree of vortex polarization. Our investigations shed light on the complexity underlying vortex interactions and reveal, furthermore, that despite some striking similarities, classical and quantum turbulence exhibit distinct structural characteristics, even at inertial range scales. Crucially, these differences arise due to correlations between the polarization and circulation intensity within vortex clusters.

Figure 1

Typical cluster summation as functions of the cluster size for both binarized (darker) and continuum (lighter) cases, for the same ${\mathrm{\Gamma }}_j^{\left(i\right)}$ realization. Each realization is normalized by its own standard deviation to ease comparison. The shaded area highlights different properties of the summation methods.

Figure 2

Statistical moments of cluster summation for the binarized process (upper panel) and the continuum process (lower panel) as functions of the cluster size $n$. Statistical moments are shown from $p=1$ (lighter colors) to $p=8$ (darker colors).

Figure 3

ESS approach for the cluster summation scaling on the binarized (dashed) and continuum (solid) cases. Colormaps are as in Fig. 2. Inset: ESS exponents found on both cases compared to the Gaussian values $p/2$ (dashed).

Figure 4

Continuum cluster summation's variance is shown in the upper frame, while its subtracted version is shown in the bottom frame. Dashed lines are power-law fits while the shaded region represents a $2\sigma$-confidence interval of the data.

Figure 5

Standardized circulation PDFs of cluster summation for various cluster sizes.

Figure 6

Two-point correlation of the detected vortex circulation as a function of the intervortex distance.