Superfluid Turbulence in the Low Temperature Regime

低温状态下的超流体湍流

• 批准号: 0104288
• 负责人: Paul Roberts
• 金额: $ 17.13万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0104288&HistoricalAwards=false
• 关键词: Superfluid; Turbulence; Low; Temperature; Regime

SUPERFLUID TURBULENCE IN THE LOW TEMPERATIRE REGIME The two most common approaches to study of superfluid turbulence are the HVBK theory and the classical theory of vortex filaments. There are many shortcomings in these models that make them unrealistic and ad hoc. The main objective of our proposal is to use a third approach based on certain forms of nonlinear Schroedinger equation (NLS) for two closely related purposes: to provide microscopically realistic parameters for HVBK theory and the classical theory of vortex filaments and to elucidate superfluid turbulence using new variants of the NLS that are more faithful to real helium II. More specifically we plan: (1) use NLS equations to study the process of vortex line reconnection in sufficient detail to characterize quantitatively the accompanying radiation of sound and Kelvin waves. The results will allow us to define reconnection rules that could be used when classical theory is applied to superfluid turbulence. (2) Use NLS theory to simulate superfluid turbulence in the low temperature regime to study the transition between weak and strong turbulence states in the superfluid. (3) Analyze dissipative NLS models that include damping from the mutual friction between superfluid and normal fluid. (4) Study and classify attractors, bifurcation sequences, and routes to chaos in solutions of forced and dissipative NLS equations. Our main goal is, however, to elucidate superfluid turbulence in the low temperature regime in which experiments are currently in the planning stage. Superfluid turbulence has been studied experimentally for many years and has by now become a major branch of cryogenic physics. In addition to the intrinsic intellectual challenges of the subject, there are several reasons for this. Helium is used as a coolant for superconducting magnets and for infrared detectors, to name just two of several engineering applications. The flow commonly becomes turbulent in these contexts. The subject also has implications beyond the field of helium research, such as in the study of high temperature superconductivity, systems of magnetic spins, melting transitions of crystals, and the origin of glitches in neutron star rotations. Superfluid turbulence may also provide insights into classical fluid turbulence, especially at high Reynolds numbers, where the vorticity has an intermittent, fractal character.

研究超流湍流最常用的两种方法是HVBK理论和经典涡丝理论。这些模型有许多缺点，使它们不切实际，而且是临时的。我们的建议的主要目的是使用第三种方法的基础上的某些形式的非线性薛定谔方程（NLS）的两个密切相关的目的：提供微观现实的参数HVBK理论和经典理论的涡丝和阐明超流湍流使用新的变种的NLS更忠实于真实的氦II。更具体地说，我们计划：（1）利用NLS方程对涡线重联过程进行了详细的研究，定量地描述了伴随的声波和Kelvin波的辐射。结果将使我们能够定义重联规则，可用于经典理论时，适用于超流湍流。(2)利用NLS理论模拟超流湍流在低温区的流动，研究超流中弱湍流态和强湍流态的转变。(3)分析耗散的NLS模型，包括超流体和正常流体之间的相互摩擦阻尼。(4)研究和分类吸引子，分岔序列，并在强迫和耗散NLS方程的解的混沌路线。然而，我们的主要目标是阐明超流湍流在低温制度中的实验目前处于规划阶段。 超流湍流的实验研究已有多年，现已成为低温物理学的一个主要分支。除了这门学科固有的智力挑战外，还有几个原因。氦被用作超导磁体和红外探测器的冷却剂，这只是几个工程应用中的两个。在这些情况下，流动通常变得湍流。这个主题也有超出氦研究领域的影响，例如在高温超导性，磁自旋系统，晶体熔化过渡和中子星星旋转故障的起源的研究。超流湍流也可以提供对经典流体湍流的见解，特别是在高雷诺数下，其中涡量具有间歇性的分形特征。