无旋流中被动标量和磁输运的平均场扩散系数
Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows
摘要：
湍流被动标量输运和平均场电动力学的平均场论的某些方面被认为是特别强调可压缩流体方面。它表明，在可压缩流中的被动标量输运的总平均场扩散系数可能小于分子扩散系数。这完全类似于一个旧的发现，关于磁平均场扩散率在导电的恶性运动的可压缩流体。如果运动的无旋部分占主导地位的旋涡部分，Pèclet或磁雷诺数不是太大，而且，此外，流动模式的变化是缓慢的，这些现象就会发生。对于被动标量和磁性的情况下，几个进一步的分析结果的平均场扩散系数和相关的数量内发现的二阶相关近似，以及通过测试场的方法，适用于独立的这种近似得到的数值结果。特别注意的是非本地和非瞬时的连接之间的连续性引起的条款和平均场。本文详细地研究了两个无旋流动的例子，在这两个例子中，出现了上述意义上的有趣现象。特别是，它表明，在这些流量的影响下，在可压缩流体中的平均标量的衰减可以比没有任何流量慢得多，并可以强烈影响所谓的记忆效应，即，相关的平均场系数取决于衰减率本身的事实。
英文摘要：
Certain aspects of the mean-field theory of turbulent passive scalar transport and of mean-field electrodynamics are considered with particular emphasis on aspects of compressible fluids. It is demonstrated that the total mean-field diffusivity for passive scalar transport in a compressible flow may well be smaller than the molecular diffusivity. This is in full analogy to an old finding regarding the magnetic mean-field diffusivity in an electrically conducting turbulently moving compressible fluid. These phenomena occur if the irrotational part of the motion dominates the vortical part, the Pèclet or magnetic Reynolds number is not too large, and, in addition, the variation of the flow pattern is slow. For both the passive scalar and the magnetic cases several further analytical results on mean-field diffusivities and related quantities found within the second-order correlation approximation are presented, as well as numerical results obtained by the test-field method, which applies independently of this approximation. Particular attention is paid to non-local and non-instantaneous connections between the turbulence-caused terms and the mean fields. Two examples of irrotational flows, in which interesting phenomena in the above sense occur, are investigated in detail. In particular, it is demonstrated that the decay of a mean scalar in a compressible fluid under the influence of these flows can be much slower than without any flow, and can be strongly influenced by the so-called memory effect, that is, the fact that the relevant mean-field coefficients depend on the decay rates themselves.
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