INSPIRE: Statistical State Dynamics of Turbulent Systems

INSPIRE奖的部分资金来自美国国家科学基金会地球科学局(GEO)大气和地球空间科学部的气候和大尺度动力学计划，以及美国国家科学基金会数学和物理科学局(MPS)物理部的等离子体物理计划。该项目的目标是发展一种关于湍流和大尺度相干结构之间关系的理论，该理论可以非常普遍地应用于大气环流、等离子体物理、行星形成和行星磁场生成等学科的各种问题。这项工作基于随机结构稳定性理论(SSST)，这是首席研究员在地球物理流体动力学的背景下发展起来的理论框架。SSST方法框架用于建立湍流和相干结构相互作用的方程，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动和波动之间的相互作用而形成的急流时，它预测了从作为线性不稳定的急流出现到有限幅度平衡，然后是作为湍流强度等参数的函数的一系列特定结构分叉的整个分叉结构，以及极限环和混沌平均状态行为的存在。这里讨论的理论的应用包括行星大气中纬向喷流的形成，环面受限等离子体中喷流的形成，行星的自持磁场，伴随流向滚滚和条纹的边界层湍流(气象学和海洋学中感兴趣的)，以及行星形成所需的开普勒盘中湍流角动量传输的维持。该项目具有更广泛的科学影响，因为它试图为几个科学学科中目前不被认为具有相同基础结构和动力学的现象确定统一的原理。所开展工作的统一性和跨学科性质是通过激励机制为该项目提供资金的理由。

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.