对流扩散方程混合效率的一个界
A Bound on Mixing Efficiency for the Advection-Diffusion Equation
摘要：
本文导出了一个被动标量在对流和扩散作用下与体源混合效率的上界。对于一个给定的搅拌速度场，混合效率的测量方面的等效扩散率，这是分子扩散率，将需要实现相同水平的波动的标量浓度在搅拌的情况下，对于相同的源分布。等效扩散率的界限仅取决于源和平流场的函数“形状”。直接数值模拟进行了一个简单的平流测试的界限。
英文摘要：
An upper bound on the mixing efficiency is derived for a passive scalar under the influence of advection and diffusion with a body source. For a given stirring velocity field, the mixing efficiency is measured in terms of an equivalent diffusivity, which is the molecular diffusivity that would be required to achieve the same level of fluctuations in the scalar concentration in the absence of stirring, for the same source distribution. The bound on the equivalent diffusivity depends only on the functional "shape" of both the source and the advecting field. Direct numerical simulations performed for a simple advecting flow to test the bounds are reported.
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