Hydrodynamics & Magnetohydrodynamics

小行星9600060 理想流体湍流的统计平衡模型的最新进展表明，它们具有比以前认为的更大的预测能力。 与传统的均匀湍流理论不同，这些模型捕捉了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，它们为在微观无序中持续存在的相干结构提供了确定的宏观方程。 拟议的调查解决这些统计均衡模型的制定，理由和解决方案。 这项工作的目标是回答从流体力学和磁流体力学的原型模型的基本问题。 分析和数值方法。 在理论方面，连续和晶格模型的构建，并建立其属性使用的x-空间和k-空间方法的合成。 这种方法有望产生新的理论的湍流松弛均匀和分层的流体，不可压缩的磁流体在二维和三维。 在计算方面，优化方法的目的是解决约束最大熵问题，管理各种模型。 这些数值方法的实施，以揭示模型的预测，特别是在实验或模拟可用于比较的设置。 %%% 流体的紊流是物理科学中尚未解决的难题之一。 对它有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手段。 从空气动力学设计到天气预报，许多应用领域都需要这样的计算。 类似地，等离子体（热的电离气体）的建模，例如在聚变能量研究中出现的，需要磁场中导电流体的湍流理论。 拟议中的工作是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性，主要状态，而不解决其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，目前只有 在一些简化的系统中。 调查的动机是扩大这些工具的应用范围，并通过完整的理论和有效的计算方法来支持它们。 ***

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. ***