湍流输送中的记忆效应
Memory effects in turbulent transport
摘要：
在磁场的平均场论中，湍流输运，即湍流电动势，由α效应和湍流磁扩散的组合来描述，其通常被假设为分别与平均场及其空间导数成比例。对于被动标量，只有湍流扩散，其中平均浓度通量取决于平均浓度梯度。然而，这些比例是近似值，只有当平均场或平均浓度随时间缓慢变化时才有效。湍流运输具有记忆，即它在很大程度上取决于过去的历史的平均场的例子。这样的效果被捕获通过替换湍流传输系数与时间积分内核，导致传输系数，有效地依赖于平均场本身的频率或增长率。在本文中，我们进行数值实验，找到这种效果的特征时间尺度（或记忆长度），以及简单的分析模型的积分内核的情况下，被动标量浓度和运动发电机。积分核然后可以用来找到自洽的增长或衰减率的平均场。在平均场发电机中，基于α效应和湍流扩散系数的稳态值的增长率和周期可能与实际值有很大的不同。
英文摘要：
In the mean-field theory of magnetic fields, turbulent transport, i.e. the turbulent electromotive force, is described by a combination of the alpha effect and turbulent magnetic diffusion, which are usually assumed to be proportional respectively to the mean field and its spatial derivatives. For a passive scalar there is just turbulent diffusion, where the mean flux of concentration depends on the gradient of the mean concentration. However, these proportionalities are approximations that are valid only if the mean field or the mean concentration vary slowly in time. Examples are presented where turbulent transport possesses memory, i.e. where it depends crucially on the past history of the mean field. Such effects are captured by replacing turbulent transport coefficients with time integral kernels, resulting in transport coefficients that depend effectively on the frequency or the growth rate of the mean field itself. In this paper we perform numerical experiments to find the characteristic timescale (or memory length) of this effect as well as simple analytical models of the integral kernels in the case of passive scalar concentrations and kinematic dynamos. The integral kernels can then be used to find self-consistent growth or decay rates of the mean fields. In mean-field dynamos the growth rates and cycle periods based on steady state values of alpha effect and turbulent diffusivity can be quite different from the actual values.
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