Accession Number : ADA557276


Title :   Local Stretching Theories


Descriptive Note : Lecture 4


Corporate Author : WOODS HOLE OCEANOGRAPHIC INSTITUTION MA


Personal Author(s) : Thiffeault, Jean-Luc ; Goluskin, David ; Roy, Anubhab


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a557276.pdf


Report Date : 24 Jun 2010


Pagination or Media Count : 12


Abstract : 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.


Descriptors :   *FLUID MECHANICS , *MIXING , ADVECTION , BERNOULLI DISTRIBUTION , DIFFUSION , LAGRANGIAN FUNCTIONS , LECTURES , LYAPUNOV FUNCTIONS


Subject Categories : Fluid Mechanics


Distribution Statement : APPROVED FOR PUBLIC RELEASE