Based on the theory of the thermodynamic equilibrium in a system of quantum vortices in superfluid liquids and in a Bose – Einstein condensate in the presence of a counterflow of normal and superfluid components, we investigate the structure of a chaotic tangle of quantum vortices in turbulent superfluid liquids. Using the characteristic functional method, the properties of hydrodynamic vortex filaments are examined. It is shown that the average curvature of the vortex lines is on the order of the intervortex distance, with the proportionality coefficient being independent of the counterflow velocity. It is found that the degree of anisotropy of the vortex loops does not depend on the applied counterflow velocity. The obtained results explain the origin of the anisotropy as well as the relationship between the curvature of the lines and the intervortex space and their dependence on the parameters of the problem.

中文翻译：

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湍流超流体液体和玻色-爱因斯坦凝聚物中量子涡的混沌缠结的结构

基于超流体中量子涡旋系统中的热力学平衡理论以及在正常和超流体组分逆流的情况下，玻色-爱因斯坦凝聚物中的热力学平衡理论，我们研究了湍流超流体中量子涡旋的混沌缠结结构液体。使用特征函数方法，检查了流体动力涡流丝的性能。结果表明，涡旋线的平均曲率约为涡旋距离，比例系数与逆流速度无关。发现涡旋环的各向异性程度不取决于所施加的逆流速度。