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arXiv 2012.00312physics.plasm-phcond-mat.stat-mechphysics.ao-ph
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等离子体和大气流体中湍流的密度算符方法

Density operator approach to turbulent flows in plasma and atmospheric fluids

Konstantin G. Zloshchastiev

摘要:

我们制定了一个统计波力学方法来描述耗散和不稳定性的二维湍流的磁化等离子体和大气流体,如漂移和Rossby波。这是由于希尔伯特空间的存在,与等离子体的电势或大气流体的流函数有关。因此,我们认为这种湍流宏观波动力学现象,驱动的非厄米哈密顿算子,我们推导出,其反厄米分量归因于环境的影响。引入一个波力学密度算子的统计合奏波,我们制定主方程和定义观测:如拟能和能量的波和纬向流的统计平均值。我们确定,我们的开放系统通常可以遵循两种类型的时间演化,这取决于环境是否阻碍或协助系统的稳定性和完整性。我们还考虑了相空间制定的理论,包括几何光学极限和超越,并研究物理观测量的守恒定律。因此,它表明,该方法预测各种机制的能量和涡度拟能漂移波和纬向流之间的交换,这是迄今为止被忽视的波动动力学方程模型的基础上。

英文摘要:

We formulate a statistical wave-mechanical approach to describe dissipation and instabilities in two-dimensional turbulent flows of magnetized plasmas and atmospheric fluids, such as drift and Rossby waves. This is made possible by the existence of Hilbert space, associated with the electric potential of plasma or stream function of atmospheric fluid. We therefore regard such turbulent flows as macroscopic wave-mechanical phenomena, driven by the non-Hermitian Hamiltonian operator we derive, whose anti-Hermitian component is attributed to an effect of the environment. Introducing a wave-mechanical density operator for the statistical ensembles of waves, we formulate master equations and define observables: such as the enstrophy and energy of both the waves and zonal flow as statistical averages. We establish that our open system can generally follow two types of time evolution, depending on whether the environment hinders or assists the system's stability and integrity. We also consider a phase-space formulation of the theory, including the geometrical-optic limit and beyond, and study the conservation laws of physical observables. It is thus shown that the approach predicts various mechanisms of energy and enstrophy exchange between drift waves and zonal flow, which were hitherto overlooked in models based on wave kinetic equations.

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