Scalar and Wave Transport in Random Flows

DMS 9971322随机流中的标量和波输运加州大学戴维斯的Albert Fannjiang摘要这个项目涉及湍流中粒子、声音和磁场的输运。 本研究旨在对多尺度、长程相关随机流对大尺度输运的影响寻求新的、根本性的理解。 利用抽样漂移、涡动扩散、变分原理等方法，我们证明了在某些具有长程相关的随机流中存在非马尔可夫输运（如分数布朗运动），它是马尔可夫输运（如布朗运动）的另一种宏观输运模型。 对于波的输运，我们提出了一个相空间的方法，通过维格纳变换。 我们知道，一个中等范围的声音频率与流场耦合：它们通过相互散射和拉伸相互转换。 波在长时间内的传输可以用辐射传输方程来描述，而在流体流动中的传输是普遍存在的。 粒子和波的输运是影响环境和全球变化的重要机制之一，也是化学工程和材料加工中的基本过程。自然流动或工程流动是非常复杂的，主要是由于存在许多不同长度尺度的现象。我们用一种严格的、新颖的方法研究了标准模型中的多尺度现象。 本文介绍了一个新的框架、概念和方法，这对于理解一般多尺度流体的输运是非常有用的。

DMS 9971322Scalar and Wave Transport in Random FlowsAlbert FannjiangUniversity of California DavisABSTRACTThis project concerns the transport of particles, sound and magneticfields in turbulent flows. This study seeks new, fundamentalunderstanding of the the effect of the multiscaled, long-rangecorrelated random flows on large scale transport. Using the ideas ofsampling drift, eddy diffusivity, variational principles and othermethods we show that non-Markovian transport, such as fractionalBrownian motions, arises in certain random flows with long-rangecorrelations, and it stands as an alternative macro-transport model toMarkovian transport, such as Brownian motion. For wave transport, wepropose a phase-space approach by means of the Wigner transform. Weshow that a middle range of sound frequencies couples with the flowfield: they convert into each other through mutual scattering andstretching. Transport of waves at long times can be described byradiative transfer equations.Transport in fluid flows is ubiquitous. Transport of particles andwaves is among the most important mechanisms affecting environment orglobal change; it is also a fundamental process in chemical engineeringand materials processing. Natural or engineering flows are verycomplicated due to primarily the presence of phenomena of manydifferent length scales. We study these multiple-scale phenomena for astandard model by a rigorous, novel approach. We introduce a newframework, concepts and methods which will be very useful forunderstanding transport in general fluids with multiple scales.