Intermittency and coherent structures in ionospheric and magnetospheric turbulence a nonperturbative: a nonperturbative approach to space plasma transport

Batchelor和Townsend（1949）可能是第一个报道小尺度高雷诺数Navier-Stokes湍流是间歇性的。我们现在坚信，间歇性可能是pdf中存在非高斯尾的原因。传统的方法是用扰动的方法来处理湍流问题。传统模型未能抓住间歇性的本质。的确，许多现象，在物理学的各个领域，特别是在等离子体物理学中，通过pdf中的尾巴来表现自己。挑战在于开发能够从非线性偏微分方程中提取pdf的数学模型。其中一个模型是在量子力学和量子场论（t'Hooft）中首先提出的“瞬子”模型。我们建议将“瞬子”形式应用于发生在极光E区和F区的电离层湍流问题，以及发生在极光加速区的离子声湍流问题。我们建议应用和开发合适的非摄动技术来首先观察电离层湍流，由非常类似于Hasegawa-Wakatani方程的偏微分方程描述。我们的第一步是将瞬子形式化应用于非耗散情况，其中已知存在精确的非线性相干结构。第二步将包括耗散机制并评估其对非耗散解的影响。第三步将包括提取pdf并计算所需的力矩，以建立与电离层和极光加速观测比较的基础。

Batchelor and Townsend (1949) were probably the first ones to report that small scales of high-Reynolds number Navier-Stokes turbulence were intermittent. We now strongly believe that intermittency might be the cause behind the existence of non-Gaussian tails in the PDFs. The conventional  approach has consisted of treating the turbulence problems perturbatively. The conventional models have failed to catch the essence of intermittency. Indeed, many phenomena, in various fields of physics and in plasma physics in particular, manifest themselves through a tail in the PDFs. The challenge is to develop mathematical models that enable the extraction of PDFs from nonlinear partial differential equations. One such model is the "Instanton" model first developed in Quantum Mechanics and Quantum Field Theory (t'Hooft). We propose to apply the "Instanton" formalism to the problem of ionospheric turbulence as it occurs in the auroral E and F regions and to the problem of ion acoustic turbulence as it occurs in the auroral acceleration region. We propose to apply and develop suitable nonperturbative techniques to first look at ionospheric turbulence, described by PDEs very similar to the Hasegawa-Wakatani equations. Our first step will be to apply the Instanton formalism to the non-dissipative case, where exact nonlinear coherent structures are known to exist. The second step will consist of including the dissipation mechanisms and assessing their impacts on the nondisspative solution. The third step will consist of extracting the PDFs and calculating the needed moments to establish a base for comparison with ionsopheric and auroral acceleration observations.