INSPIRE: Statistical State Dynamics of Turbulent Systems

该INSPIRE奖部分由NSF地球科学理事会（GEO）大气和地球空间科学部的气候和大规模动力学计划资助，和美国国家科学基金会数学和物理科学理事会（MPS）物理部的等离子体物理计划。该项目的目标是发展一种理论，解释湍流和大尺度湍流之间的关系。尺度相干结构，可以非常普遍地应用于学科中的各种问题，包括大气环流，等离子体物理，行星形成和行星磁场的产生。 这项工作是基于随机结构稳定性理论（SSST），这是一个理论框架，主要研究者已经开发的地球物理流体动力学的背景下。 SSST方法框架用于创建湍流和相干结构的相互作用的方程，并且方程的平衡解识别系统的统计平均状态。 例如，当该理论应用于由于纬向平均大气流和波动之间的相互作用而形成的喷流时，它预测了从喷流出现作为线性不稳定到有限振幅平衡的整个分叉结构，随后是作为参数（例如湍流强度）的函数的一系列特定的结构分叉，以及极限环和混沌平均态行为的存在性。 该理论的应用包括行星大气中纬向喷流的形成、环形约束等离子体中喷流的形成、行星的自持磁场、边界层湍流伴随流向卷和条纹（对气象学和海洋学感兴趣），以及维持行星形成所需的开普勒圆盘中的湍流角动量传输。该项目具有更广泛的科学影响因为它试图为目前不被认为具有相同的基本结构和动力的几个科学学科中的现象确定统一的原则。 所要开展的工作具有统一性和跨学科性质，这是通过INSPIRE机制为该项目供资的理由。

This INSPIRE award is partially funded by the Climate and Large-scale Dynamics Program in the Division of Atmospheric and Geospace Science of the NSF Directorate for Geosciences (GEO), and the Plasma Physics Program in the Physics Division of the NSF Directorate for Mathematical and Physical Sciences (MPS).The goal of the project is to develop a theory for the relationship between turbulence and large-scale coherent structures that can be applied very generally to a variety problems in disciplines including atmospheric circulation, plasma physics, planet formation, and the generation of planetary magnetic fields. The work is based on stochastic structural stability theory (SSST), a theoretical framework which the Principal Investigator has developed in the context of geophysical fluid dynamics. The SSST method framework is used to create equations for the mutual interaction of turbulence and coherent structures, and the equilibrium solutions of the equations identify the statistical mean states of the system. For example, when the theory is applied to the formation of jet streams due to interactions between the zonal-mean atmospheric flow and wave motions, it predicts an entire bifurcation structure from jet emergence as a linear instability to finite amplitude equilibration followed by a specific series of structural bifurcations as a function of parameters, such as turbulence intensity, as well as existence of limit cycles and chaotic mean state behavior. Applications of the theory considered here include the formation of zonal jets in planetary atmospheres, jet formation in toroidally confined plasmas, the self-sustaining magnetic fields of planets, boundary layer turbulence accompanied by streamwise rolls and streaks (of interest in meteorology and oceanography), and the maintenance of turbulent angular momentum transport in Keplerian discs required for planetary formation.The project has broader scientific impacts in that it seeks to identify unifying principles for phenomena in several scientific disciplines that are not currently recognized as having the same underlying structures and dynamics. The unifying, cross-disciplinary nature of the work to be performed is the justification for funding the project through the INSPIRE mechanism.