Creation and evolution of quantum turbulence in novel geometries

湍流在真实的世界中无处不在，几乎影响着我们日常生活的方方面面，包括交通、能源生产、气候和生物过程。尽管湍流具有普遍的重要性，但人们对它的理解并不充分。理查德·费曼称之为“经典物理学中最重要的未解决的问题”。湍流很难在基本水平上理解，因为流体的湍流运动在非常宽的长度尺度范围内是复杂的。量子力学通常使复杂的问题在概念上变得简单，超流体中的量子湍流（QT）就是一个很好的例子。在低温下，超流体是最接近理想流体的近似，因为它们可以无摩擦地流动，（几乎）不可压缩，并且它们的涡旋是量子化的，使得它们都是相同的。像经典湍流一样，QT是一种非平衡现象：去除驱动力，它会衰减--尽管在He II中可能不完全，因为残留的量子化涡旋亚稳态地钉在壁上。在He II中，QT的形成通常似乎是由这种对流涡旋“播种”的。早期的振荡结构实验已经暗示，随着振荡幅度的增加，进化到完全发育的QT可能至少经过两个阶段。(i)在第一临界速度以上，被钉扎线的摇动产生涡旋缠结，其中运动仅发生在与线间距相当的长度尺度上。(ii)在较高的临界速度下，发生第二次转变，其中缠结的层流分解成湍流，就像经典流体中的流动一样。我们现在提出两个密切相关的实验，每个实验都利用新技术，首先是探索对流涡旋的基本特性，其次是，研究在没有回流涡的情况下，内禀涡的产生过程。第一组实验将探索在一个药丸盒内的超流体中的涡核，形状的细胞，其中当细胞围绕其对称轴振荡时，凸表面上没有流动。我们预计，细胞运动产生开尔文波的revelocity涡，如果他们被钉在平行的面，导致在临界速度以上的重连和创建准经典的旋涡纠缠在层流。在超流体中没有凸面意味着第二临界速度，导致完全发展的QT将被提高，使其能够被解决。我们还将研究对流涡旋的钉扎。在有限的温度下，我们可以预期，热涨落将使线顺序地去钉扎/重新钉扎，使其末端滑过表面，而在T=0时，线将在钉扎位点上冻结。然而，加州大学戴维斯分校的测量结果对这一被广泛接受的观点提出了质疑，认为随着温度的下降，福尔斯的钉扎作用会减少，即与预期相反。我们将解决这个谜，并试图从理论上解释我们的发现。在第二组实验中，我们将研究一个小型磁悬浮超导球体通过超流体的各种运动。虽然以前没有人尝试过这样做，但我们有信心能够振荡球体（与早期的实验接触），并且第一次能够以稳定的速度在圆周上移动它。作为时间函数的阻力的测量将提供关于钉扎涡环的存在/不存在及其作为自由涡环的增长和分离的信息，作为速度和温度的函数。我们设想这些实验在超流体中量子化涡旋线的研究中开辟新的篇章，非常普遍，而不仅仅是在He-4中。飞行球实验将为可能的低温“风洞”铺平道路，在该风洞中，悬浮模型结构通过静止的He-4移动，雷诺数高达100，000，000。

Turbulence is ubiquitous in the real world and affects almost every aspect of our daily lives, including transport, energy production, climate, and biological processes. Despite its universal importance, turbulence is not well understood. Richard Feynman called it the "most important unsolved problem of classical physics". Turbulence is hard to understand at a fundamental level because of the complexity of turbulent motion of the fluid over an extremely wide range of length scales. Quantum mechanics often makes complex problems conceptually simpler, and quantum turbulence (QT) in superfluids is a prime example. At low temperatures, superfluids are the closest attainable approximation to an ideal fluid in that they can flow without friction, are (almost) incompressible, and their vortices are quantised, making all of them identical.Like classical turbulence, QT is a non-equilibrium phenomenon: remove the driving force, and it decays - though perhaps not completely in He II due to residual quantised vortices pinned metastably to the walls. In He II, the creation of QT usually seems to be "seeded" by such remanent vortices. Earlier experiments on oscillating structures have hinted that evolution to fully-developed QT as the oscillatory amplitude increases may occur via at least 2-stages. (i) Above a first critical velocity, shaking of the pinned lines creates a vortex tangle where motion only occurs on length scales comparable with the line spacing. (ii) At a higher critical velocity, a second transition occurs in which laminar flow of the tangle breaks down into turbulence, like flow in a classical fluid. We now propose two closely-related experiments, each utilising novel technology, first to explore the fundamental properties of the remanent vortices and, secondly, to investigate the intrinsic vortex creation process in the absence of remanent vortices.The first set of experiments will explore vortex nucleation in superfluid within a pill-box-shaped cell where there is no flow over convex surfaces when the cell is oscillated about its axis of symmetry. We expect the cell movements to generate Kelvin waves on remanent vortices if they are pinned to the parallel faces, resulting in reconnections above a critical velocity and creation of the quasi-classical vortex tangle in laminar flow. The absence of a convex surface within the superfluid means that the second critical velocity, leading to fully developed QT will be raised, enabling it to be resolved. We will also investigate the pinning of remanent vortices. At finite temperature, we might expect that thermal fluctuations will enable a line to de-pin/re-pin sequentially, sliding its end across the surface whereas, at T=0, the lines would become frozen on pinning sites. However, measurements at UC Davis have questioned this widely-accepted picture, suggesting decreased pinning as the temperature falls, i.e. the opposite of expectation. We will resolve this enigma and will try to account theoretically for what we find. In the second set of experiments, we will study diverse motions of a small, magnetically-levitated, superconducting sphere through the superfluid. Although nothing like this has been attempted previously, we are confident of being able to oscillate the sphere (to make contact with earlier experiments) and, for the first time, to be able to move it in a circle at a steady velocity. Measurements of the drag as a function of time will provide information about the presence/absence of pinned vortex loops and their growth and separation as free vortex rings, as functions of velocity and temperature. We envisage these experiments opening a new chapter in the study of quantized vortex lines in superfluids, quite generally, not just in He-4. The flying sphere experiments will prepare the way for a possible cryogenic "wind tunnel" where a levitated model structure is moved through stationary He-4, with Reynolds numbers up to 100,000,000.