论文标题
在宽阔的通道中，被动标量的运输具有表面地形
Transport of a passive scalar in wide channels with surface topography
论文作者
论文摘要
我们将被动标量的经典分散理论推广，以得出渐近长期对流 - 扩散方程，以悬浮在宽，结构化的通道中，并受到稳定的低雷诺兹空剪切流的影响。我们的理论对通道的小粗糙度幅度有效，可作为傅立叶序列扩展的一般表面形状。我们确定各向异性分散张量，该张量取决于表面结构的特征波长和振幅。对于相对于所应用的流动方向倾斜的表面，我们发现沿主要方向（即，分散量张量的主要特征向量）的分散剂与主要流动方向的角度相比，相对于经典的泰勒分散剂而变得增强。相比之下，与颗粒的短时扩散率相比，垂直于其的色散可以减少。此外，对于以傅立叶分解为代表的任意表面形状，我们发现每个傅立叶模式都以线性独立的校正对经典的泰勒分散张量进行线性独立校正。
We generalize classical dispersion theory for a passive scalar to derive an asymptotic long-time convection-diffusion equation for a solute suspended in a wide, structured channel and subject to a steady low-Reynolds-number shear flow. Our theory, valid for small roughness amplitudes of the channel, holds for general surface shapes expandable as a Fourier series. We determine an anisotropic dispersion tensor, which depends on the characteristic wavelengths and amplitude of the surface structure. For surfaces whose corrugations are tilted with respect to the applied flow direction, we find that dispersion along the principal direction (i.e., the principal eigenvector of the dispersion tensor) is at an angle to the main flow direction and becomes enhanced relative to classical Taylor dispersion. In contrast, dispersion perpendicular to it can decrease compared to the short-time diffusivity of the particles. Furthermore, for an arbitrary surface shape represented in terms of a Fourier decomposition, we find that each Fourier mode contributes at leading order a linearly-independent correction to the classical Taylor dispersion tensor.
