{'fraction_non_alphanumeric': 0.033783783783783786, 'fraction_numerical': 0.005405405405405406, 'mean_word_length': 5.557522123893805, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Transition from non-swirling to swirling axisymmetric turbulence

Strictly axisymmetric turbulence, i.e., turbulence governed by the Navier-Stokes equations modified such that the flow is invariant in the azimuthal direction, is a system intermediate between two-and three-dimensional turbulence. We investigate statistically steady states of this system by direct numerical simulation using a forcing protocol, which allows the injected energy in the toroidal and in the poloidal directions to be tuned independently. A sharp transition between a two-dimensional two-component (2D2C, non-swirling) flow and a two-dimensional three-component (2D3C, swirling) flow is observed. We derive a statistical model which reproduces this transition.