Microscopic dynamics of quantized vortices in turbulent superfluid in the T=0 limit

湍流在自然界中无处不在，几乎影响着我们日常生活的方方面面。尽管湍流具有压倒性的重要性，但人们对它的了解却很少，这主要是因为湍流运动在很宽的长度尺度范围内的复杂性。超流氦中的湍流，被称为量子湍流，是特殊的，因为量子力学限制所有的旋涡都有一个固定的循环值。因此，我们处理的是一个动态的涡旋线缠结，所有的涡旋线都具有相同的强度。湍流及其量子变体是一种内在的非平衡现象：去除驱动力，湍流衰减，我们的目标是在T=0极限下面对量子湍流剩下的两个相互关联的挑战：（i）观察和研究体缠结中单个涡线发生的基本过程;（ii）探讨涡线与固体边界的相互作用及其后果。(i)在0.5K以下，涡线运动的阻尼有效地消失。虽然人们预计，在广泛的长度尺度上的涡旋重联和变形是其动力学的主要成分，但迄今为止，还没有在低温下对这些进行直接观测。该计划将产生涡旋线的2D和3D图像序列，它们的束和缠结-在不同类型的湍流中，通过He 2 * 准分子或染色纳米颗粒作为示踪剂的荧光可视化。因此，我们将获得有关量子湍流的不同方面的信息，以及它与经典湍流的区别。这项新技术可能会彻底改变量子湍流的研究。由于量子湍流在大尺度上模仿经典湍流，我们对集中涡度区域的结构和动力学的直接可视化也可能对理解相干结构引起罕见的大振幅事件时经典湍流中的不稳定性做出重要贡献。(ii)对固壁附近涡缠结动力学的理解是另一个突出的基本问题。量子湍流的产生似乎是由超流体中预先存在的对流涡旋“播种”的。有人建议，充分发展的量子湍流的振荡结构的振幅增加的演变可能会发生通过一个2阶段的过程。首先，线的晃动会使小涡环的气体脱落，这些小涡环会重新连接，形成随机的缠结。这种缠结本身的行为就像一种经历层流的小粘度流体。然后，在较高的速度下，当流动变成湍流时，存在第二转变。我们建议用实验来检验这一图景。所有早期关于振荡结构产生量子湍流的实验都使用具有凸面的物体;它们周围的流动在低速时是经典不稳定的，因此这两个假设的转变并没有明显分开。相比之下，我们提出的实验中，氦气是一个药丸盒内，围绕其轴振荡，从而消除了所有的流动凸表面。然后，随着阻尼特性的增加，这两个过渡应该很好地分离和识别。我们还将通过研究它们对微观突起的钉扎来阐明对流涡旋本身的基本性质。最近的测量结果表明，涡旋钉扎在低温下变得较弱，可能是通过与对流涡旋网格线的重新连接。为了测试这些结果，我们提出了实验在一个球形的细胞，几何形状中，钉扎涡环是固有的不稳定，以及可视化的reflections涡，远离和附近的边界。

Turbulence is ubiquitous in nature and affects almost every aspect of our daily lives. Despite its overwhelming importance, turbulence is poorly understood, mainly because of the complexity of turbulent motion over a very wide range of length scales. Turbulence in superfluid helium, known as quantum turbulence, is special, because quantum mechanics restricts all vortices to have a single fixed value of circulation. Thus we are dealing with a dynamic tangle of vortex lines, all of the same strength. Turbulence, including its quantum variant, is an inherently non-equilibrium phenomenon: remove the driving force, and the turbulence decays.Our goal is to confront the two remaining, mutually interconnected, challenges of quantum turbulence in the T=0 limit: (i) to observe and investigate the elementary processes occurring with individual vortex lines inside bulk tangles; (ii) explore the interaction, and its consequences, of vortex lines with solid boundaries. (i) Below 0.5K damping of the motion of vortex lines effectively vanishes. While it is expected that vortex reconnection and deformation on a broad range of length scales are the main ingredients of their dynamics, no direct observations of these at low temperatures have been made so far. The programme will produce sequences of 2D and 3D images of vortex lines, their bundles and tangles - in different types of turbulent flow, visualized through fluorescence of either He2* excimers or dyed nanoparticles as tracers. Hence, we will obtain information on different aspects of quantum turbulence, and its distinction from classical turbulence. This new technique could revolutionize the study of quantum turbulence. As quantum turbulence mimics classical turbulence on large length scales, our direct visualization of the structure and dynamics of the region of concentrated vorticity might also make an important contribution to the understanding of intermittency in classical turbulence when coherent structures cause rare events of large amplitude.(ii) The understanding of the dynamics of vortex tangles near solid walls is another outstanding fundamental question. The creation of quantum turbulence seems to be "seeded" by remanent vortices pre-existing in the superfluid. It was suggested that the evolution to fully-developed quantum turbulence as the amplitude of an oscillating structure increases may occur via a 2-stage process. First, shaking of the lines sloughs off a gas of small vortex rings, which reconnect to form a random tangle. This tangle itself behaves like a fluid of small viscosity undergoing laminar flow. Then at a higher velocity there is a second transition when the flow turns turbulent. We propose to test this picture experimentally. All earlier experiments on the generation of quantum turbulence by oscillating structures have used objects with convex surfaces; the flow round them is classically unstable at a low velocity, so that the two supposed transitions are not clearly separated. In contrast, we propose experiments where the helium is inside a pill-box that oscillates about its axis, thus eliminating all flow over convex surfaces. The two transitions should then be well separated and identifiable as characteristic increases in damping. We will also illuminate the fundamental properties of the remanent vortices themselves, by investigating their pinning to microscopic protuberance. Recent measurements indicate that vortex pinning get weaker at low temperatures, perhaps through reconnections with lines of the mesh of remanent vortices. To test these results, we propose experiments in a spherical cell, a geometry in which pinned vortex loops are inherently unstable, as well as visualization of remanent vortices, both away from and near boundaries.