Vortex clustering, polarisation and circulation intermittency in classical and quantum turbulence

Abstract

The understanding of turbulent flows is one of the biggest current challenges in physics, as no first-principles theory exists to explain their observed spatio-temporal intermittency. Turbulent flows may be regarded as an intricate collection of mutually-interacting vortices. This picture becomes accurate in quantum turbulence, which is built on tangles of discrete vortex filaments. Here, we study the statistics of velocity circulation in quantum and classical turbulence. We show that, in quantum flows, Kolmogorov turbulence emerges from the correlation of vortex orientations, while deviations—associated with intermittency—originate from their non-trivial spatial arrangement. We then link the spatial distribution of vortices in quantum turbulence to the coarse-grained energy dissipation in classical turbulence, enabling the application of existent models of classical turbulence intermittency to the quantum case. Our results provide a connection between the intermittency of quantum and classical turbulence and initiate a promising path to a better understanding of the latter.

Turbulence in rotating Bose-Einstein condensates

“…In this regime a thermal counterflow is believed to play an important role in the dynamics. This scaling was also found in numerical simulations with counterflow [15,16], but more intriguingly, also more recently in simulations of BECs with an initial array of ordered vortices and no apparent counterflow [17,18], as well as in simulations of homogeneous superfluid turbulence [19].…”

“…A k −1 scaling has been associated before to the presence of a counterflow [12], to flux-less solutions [43], or to disorganized vortex tangles [19,44]. In our case, the flux of energy towards small scales in the presence of rotation is substantially decreased, as evidenced by the accumulation of energy at large scales, and also by direct computation of the flux (not shown).…”

“…However, and unlike homogeneous quantum turbulence, the ∼ k −1 scaling of the incompressible kinetic energy in the rotating case cannot be the result of unpolarized bundles of vortices (i.e., of randomly and independently oriented vortices [19,44]). As explained before, the vortices in the rotating BEC must be polarized, and more or less aligned in order to approximate the solid body rotation.…”

“…However, for a disorganized state with random positions, the sum in Eq. ( 10) reduces to the sum of the spectra of individual vortices, each with a ∼ k −1 scaling [6,19].…”

Statistics of Extreme Turbulent Circulation Events from Multifractality Breaking

“…More recently, considerable hardware improvements have enabled the implementation of DNS at much higher Reynolds numbers, so that a vivid interest in the problem of turbulent circulation statistics has resurfaced in the literature [10][11][12][13][14][15], even driving further perspectives in the understanding of quantum turbulence [16,17]. The deadlock of numerical issues was broken by a computational tour de force performed by Iyer et al [10,14], who have identified a number of relevant statistical aspects of the turbulent circulation Γ, summarized as follows: (i) Exponents of its statistical moments depart more clearly from the Kolmogorovian-like predicted values at high orders, where they become linearly dependent on the moment orders;…”