DTIC ADA557276: Local Stretching Theories pdf

DTIC ADA557276: Local Stretching Theories

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In this lecture we will try to understand local or Lagrangian theories involved in mixing of passive scalars. This involves solving the advection-diffusion (AD) equation along fluid trajectories. The origins of these local theories can be traced to Batchelor’s idea of describing the flow via spatially-constant strain-rate matrices with prescribed time dependence. Kraichnan addressed the problem next by considering the velocity field in the AD equation to be a stochastic Gaussian field with a time correlation that decays infinitely rapidly (or is white in time) and a spatial correlation that has a power-law structure. This led to solving a stochastic differential equation. Zeldovich encountered the problem in the context of heat diffusion and the magnetic dynamo and adopted a random matrix theory approach. More recently, tools from large deviation theory and path integration have aided in obtaining a complete solution of the problem, as will be discussed in this lecture

• Creator/s: Defense Technical Information Center
• Date: 6/24/2010
• Year: 2010
• Book Topics/Themes: DTIC Archive, , WOODS HOLE OCEANOGRAPHIC INSTITUTION MA, *FLUID MECHANICS, *MIXING, ADVECTION, BERNOULLI DISTRIBUTION, DIFFUSION, LAGRANGIAN FUNCTIONS, LECTURES, LYAPUNOV FUNCTIONS

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