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

Batchelor和Townend(1949)可能是第一个报告高雷诺数的小尺度Navier-Stokes湍流是间歇性的。我们现在强烈认为，间歇性可能是PDF中存在非高斯尾部的原因。传统的计算方法包括微扰地处理湍流问题。传统的模型未能抓住间歇性的本质。事实上，在物理学的各个领域，特别是在等离子体物理学中，许多现象都是通过PDF中的尾巴表现出来的。挑战是开发能够从非线性偏微分方程式中提取PDF的数学模型。其中一个模型是最先在量子力学和量子场论(t‘Hooft)中发展起来的“瞬变”模型。我们建议将“瞬变”形式应用于发生在极光E和F区的电离层湍流问题和发生在极光加速区的离子声湍流问题。我们建议应用和发展合适的非微扰技术来首先研究电离层湍流，它由偏微分方程组描述，非常类似于长谷川-Wakatani方程。我们的第一步将是将Instanton形式应用到非耗散情况，其中确切的非线性相干结构是已知存在的。第二步将包括耗散机制，并评估它们对非耗散解决方案的影响。第三步将包括提取PDF和计算所需的矩，以建立与电离层和极光加速观测进行比较的基础。

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.