Local Stretching Theories

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.

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Document Details

Document Type
Technical Report
Publication Date
Jun 24, 2010
Accession Number
ADA557276

Entities

People

  • Anubhab Roy
  • David Goluskin
  • Jean-Luc Thiffeault

Organizations

  • Woods Hole Oceanographic Institution

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Advection
  • Bernoulli Distribution
  • Differential Equations
  • Diffusion
  • Eigenvalues
  • Equations
  • Flow
  • Flow Fields
  • Matrix Theory
  • Personal Information Managers
  • Power Series
  • Random Variables
  • Shear Flow
  • Stratified Fluids
  • Theorems
  • Trajectories
  • Turbulent Mixing

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.
  • Military History of the United States in the 20th Century.