随机流中惯性粒子的均匀化
Homogenization for Inertial Particles in a Random Flow
摘要：
研究了惯性粒子在含时随机速度场中运动并受分子扩散影响的均匀化问题。我们表明，在适当的假设下的速度场，惯性粒子的大尺度，长时间的行为是由一个有效的扩散方程的位置变量单独。这是通过在尺度参数中使用正式的多尺度扩展来实现的。膨胀依赖于潜在扩散的亚椭圆率。的扩散系数张量的表达式被发现，并研究其各种属性。形式的多尺度分析的结果是合理的严格使用鞅中心极限定理。我们的理论研究结果支持数值研究，我们研究的有效扩散系数的参数依赖的各种非量纲参数的问题。
英文摘要：
We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale, long--time behavior of the inertial particles is governed by an effective diffusion equation for the position variable alone. This is achieved by the use of a formal multiple scales expansion in the scale parameter. The expansion relies on the hypoellipticity of the underlying diffusion. An expression for the diffusivity tensor is found and various of its properties are studied. The results of the formal multiscale analysis are justified rigorously by the use of the martingale central limit theorem. Our theoretical findings are supported by numerical investigations where we study the parametric dependence of the effective diffusivity on the various non--dimensional parameters of the problem.
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