Characteristics of Two-Dimensional Quantum Turbulence in a Compressible Superfluid

Abstract

Under suitable forcing a fluid exhibits turbulence, with characteristics strongly affected by the fluid's confining geometry. Here we study two-dimensional quantum turbulence in a highly oblate Bose-Einstein condensate in an annular trap. As a compressible quantum fluid, this system affords a rich phenomenology, allowing coupling between vortex and acoustic energy. Small-scale stirring generates an experimentally observed disordered vortex distribution that evolves into large-scale flow in the form of a persistent current. Numerical simulation of the experiment reveals additional characteristics of two-dimensional quantum turbulence: spontaneous clustering of same-circulation vortices, and an incompressible energy spectrum with k −5/3 dependence for low wavenumbers k and k −3 dependence for high k.A critical distinction between hydrodynamic turbulence in a bulk fluid [1] and in one whose flows are restricted to two dimensions is that energy dissipation at small length scales is generally inhibited in the latter. In two-dimensional (2D) flows subject to small-scale forcing, energy flux is blocked through the small length scales and, instead, energy is transferred towards larger scales, comprising the inverse energy cascade of 2D turbulence [2,3]. Small-scale forcing may thus generate large-scale flows, as seen for instance in dispersal of atmospheric and oceanic particulates [4], flows of soap films [5,6] and plasmas [7], and Jupiter's Great Red Spot [8,9]. However, the nature of 2D turbulence in quantum fluids is less clear. Progress in 2D quantum turbulence (2DQT) may offer innovative routes to understanding quantum fluid dynamics [10,11] and aspects of the universality of 2D turbulence. Here we describe an experimental and numerical study of forced and decaying 2DQT in a dilute-gas Bose-Einstein condensate (BEC). Our primary result is the first clear evidence that three key characteristics of 2D turbulence may also simultaneously appear in systems exhibiting 2DQT: (i) emergence of large-scale flow from small-scale forcing, seen experimentally and numerically, (ii) numerical observation of the formation of coherent vortex structures accompanying approximate enstrophy conservation [12], and (iii) numerical observation of an incompressible kinetic energy spectrum with k −5/3 dependence for low wavenumbers k and k −3 dependence for high k. Our observations are consistent with the notion that an inverse energy cascade can exist in this system. Concepts of significance for 2D turbulence and quantum fluids share a common origin. Analyzing point vortex motion in a bounded domain, Onsager proposed in 1949 that longlived vortices may develop via mergers of smaller vortices in turbulent flows of a 2D fluid, enabling the remaining vortices to move more freely and thereby maximize system entropy [13,14]. He also proposed that vortices in superfluids have quantized circulation, and implied that turbulent 2D vortex dynamics might be ideally studied in superfluids. However, experimental demonstration of 2DQT has not been repo...

Origin of the inverse energy cascade in two-dimensional quantum turbulence

“…Quantum turbulence (QT) in highly oblate Bose Einstein condensates (BECs) provides a close experimental realization of 2D turbulence through the dynamics of quantized vortices and a well-defined theoretical framework to study turbulence from the statistical properties of a quantized vortex gas. In recent years, there have been indirect experimental evidence [2] and tantalizing numerical results [3][4][5] of the existence of an inverse energy cascade that follows the Kolmogorov scaling analogously to the classical turbulence. The condensation of energy on large scales has also been investigated in decaying quantum turbulence [6][7][8].…”

“…These vortex condensates are formed by clustering of vortices of the same sign and occur through an SO (2) symmetry-breaking phase transition with negative critical temperature [10]. Recent studies of decaying QT propose that such negative temperature states can be achieved dynamically by an evaporative heating process through the annihilation of vortex dipoles (effective heating of vortices by removing the coldest ones, i.e., the smallest dipoles) [6].…”

“…This would be analogous to the Kraichnan-Kolmogorov scaling argument for the classical coarse-grained vorticity on an inertial scale r, ω r ∼ v r /r, with the eddy velocity v r ∼ r 1/3 [1]. To investigate the origin of the inverse energy cascade in driven quantum turbulence without having to concern ourselves with the compressibility effects in quantum fluids [2], we propose a driven and dissipative point vortex model as described below.…”

Macroscopic Excitations in Confined Bose–Einstein Condensates, Searching for Quantum Turbulence

“…7,8 These issues motivate the study presented in this article. We point out that there are already experimental realizations of quantum turbulence 9,10,11 as well of studies of the route to turbulence. 5,12,13 In this work, through the Gross-Pitaevskii (GP) model 14,15 of an ultracold quantum gas, and assuming that arbitrary phase-imprinted states can be generated 16,17,18,19 we present here a survey of macroscopic excitations that lead a Bose-Einstein condensate (BEC), confined in an external harmonic potential, to stationary agitated or chaotic states that, under appropriate conditions, may be considered to pass through turbulent transients or remain as such.…”

Universal statistics of point vortex turbulence

“…Neely et al 2013). In the experiments, a Bose-Einstein condensate consisting of O(10 6 ) 87 Rb atoms is confined by a trapping potential, and is excited by the application of a magnetic field.…”