INSPIRE: Statistical State Dynamics of Turbulent Systems

INSPIRE奖部分由美国国家科学基金会地球科学理事会（GEO）大气与地球空间科学部的气候与大规模动力学项目，以及美国国家科学基金会数学与物理科学理事会（MPS）物理部的等离子体物理项目资助。该项目的目标是为湍流和大规模相干结构之间的关系发展一种理论，这种理论可以非常普遍地应用于各种学科的问题，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），这是首席研究员在地球物理流体动力学背景下开发的理论框架。利用SSST方法框架建立了湍流和相干结构相互作用的方程，并用方程的平衡解确定了系统的统计平均状态。例如，当将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，它预测了整个分岔结构，从作为线性不稳定的射流出现到有限振幅平衡，然后是一系列特定的结构分岔，作为参数的函数，例如湍流强度，以及极限环和混沌平均状态行为的存在。这里考虑的理论应用包括行星大气中纬向喷流的形成，环形受限等离子体中的喷流形成，行星的自我维持磁场，边界层湍流伴随着流向滚动和条纹（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输运的维持。该项目具有更广泛的科学影响，因为它试图确定几个科学学科中现象的统一原则，这些现象目前尚未被认为具有相同的潜在结构和动力学。要执行的工作的统一的、跨学科的性质是通过INSPIRE机制资助项目的理由。

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.