论文标题
密度算子的方法用于血浆和大气流体中的湍流
Density operator approach to turbulent flows in plasma and atmospheric fluids
论文作者
论文摘要
我们制定了一种统计波动方法，以描述磁化等离子体和大气流体（例如漂移和罗斯比波）的二维湍流中的耗散和不稳定性。希尔伯特空间的存在与与血浆的电势或大气流体的流函数有关，这是可能的。因此，我们将这种湍流视为宏观波动现象，这是由我们得出的非热汉密尔顿操作员驱动的，其抗赫米特人的组成部分归因于环境的效果。我们为波浪的统计集合引入了机电密度算子，我们制定了主方程并定义可观察到的物体：例如，波和区域流的胚胎和能量作为统计平均值。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变，具体取决于环境是否阻碍或有助于系统的稳定性和完整性。我们还考虑了该理论的相空间公式，包括几何形态限制及以后，并研究物理可观察物的保护定律。因此，该方法可以预测漂移波和纬向流之间的各种能量和肠道交换的机制，迄今为止，这些机制在基于波动力学方程的模型中被忽略了。
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.
