Hydrodynamics & Magnetohydrodynamics

9600060图灵顿理想流体湍流的统计平衡模型的最新进展表明，它们具有比之前认为的更大的预测能力。与传统的均匀湍流理论不同，这些模型捕捉到了在湍流松弛过程中形成的长寿命、大尺度结构的基本特征。此外，它们还为微观无序中的共格结构提供了明确的宏观方程。拟议的调查涉及这些统计均衡模型的制定、理由和解决办法。这项工作的目标是回答有关从流体力学和磁流体力学中提取的原型模型的基本问题。采用了解析和数值相结合的方法。在理论方面，构建了连续介质模型和晶格模型，并利用x空间和k空间的综合方法建立了它们的性质。这种方法有望为均匀和分层流体以及二维和三维不可压缩磁流体产生新的湍流松弛理论。在计算方面，优化方法旨在解决支配各种模型的约束最大熵问题。这些数值方法的实施是为了揭示模型的预测，特别是在可以进行实验或模拟以进行比较的环境中。湍流流动一直是物理学界悬而未决的难题之一。对它的一个令人满意的理论理解将提供比目前可用的更强大的计算流体运动行为的方法。从空气动力学设计到天气预报，这种计算在许多应用领域都是需要的。同样，对等离子体(热的、电离气体)的建模，如聚变能量研究中出现的等离子体，需要一个关于磁场中导电流体的湍流理论。拟议的工作见KS，以开发必要的数学工具来计算这些流体和磁流体系统的持久的、主要的状态，而不是解决它们详细行为的全部复杂性。这类工具是根据统计物理学的基本概念建立的，目前只在一些简化的系统中可用。研究的动机是扩大这些工具的应用范围，并以完整的理论和有效的计算方法为其提供支持。***

9600060 Turkington Recent progress with statistical equilibrium models of ideal fluid turbulence suggests that they have greater predictive power than previously believed. Unlike traditional homogeneous turbulence theory, these models capture the essential features of the long-lived, large-scale structures that form in the process of turbulent relaxation. Moreover, they furnish definite macroscopic equations for the coherent structures that persist amidst the microscopic disorder. The proposed investigations address the formulation, justification and solution of these statistical equilibrium models. The goal of the work is to answer fundamental questions about prototype models drawn from hydrodynamics and magnetohydrodynamics. Both analytical and numerical methods are employed. On the theoretical side, continuum and lattice models are constructed, and their properties are established using a synthesis of x-space and k-space methods. This approach is expected to yield new theories of turbulent relaxation for uniform and stratified fluids, and incompressible magnetofluids in two and three dimensions. On the computational side, optimization methods are designed to solve the constrained maximum entropy problems that govern the various models. These numerical methods are implemented to reveal the predictions of the models, especially in settings where experiments or simulations are available for comparison. %%% Turbulent fluid flow remains one of the unsolved puzzles of physical science. A satisfactory theoretical understanding of it would provide much more powerful means of computing the behavior of fluid motions than is presently available. Such computations are needed in numerous applied fields, from aerodynamic design to weather prediction. Similarly, the modeling of plasmas (hot, ionized gases), such as arise in fusion energy research, requires a theory of turbulence for electrically-conducting fluids in magnetic fields. The proposed work see ks to develop the mathematical tools necessary to calculate the persistent, predominant states of these fluid and magnetofluid systems without resolving the full complexity of their detailed behavior. Tools of this kind, which are built from basic concepts in statistical physics, are currently available only in some simplified systems. The motivation for the investigations is to extend the range of applications of these tools and to support them by complete theories and effective computational methods. ***