Multifractal sets of coherent and incoherent vortices in turbulence

We numerically verify multifractal theory (Frisch and Parisi 1985) for turbulence using simulation data at a high Reynolds number. First, we propose a simple method to directly estimate the multifractal dimension $D(h)$ of vortical structures with a given Hölder exponent $h$. Thus measured $D(h)$ is in good agreement with indirectly measured experimental data. Then, we demonstrate that these structures for $h\ll 1\mathrm{/}3$ form the hierarchy of coherent eddies, while those for $h\gg 1\mathrm{/}3$ are featureless.