Possible Statistics of Two Coupled Random Fields: Application to Passive Scalar

Abstract

We use the relativity postulate of scale invariance to derive the similarity transformations between two coupled scale-invariant random fields at different scales. We find the equations leading to the scaling exponents. This formulation is applied to the case of passive scalars advected: (1) by a random Gaussian velocity field; and (2) by a turbulent velocity field. In the Gaussian case, we show that the passive scalar increments follow a log-Levy distribution generalizing Kraichnan's solution and, in an appropriate limit, a log-normal distribution. In the turbulent case, we show that when the velocity increments follow a log-Poisson statistics, the passive scalar increments follow a statistics close to log-Poisson. This result explains the experimental observations of Ruiz et al. about the temperature increments.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2000
Accession Number
ADA385328

Entities

People

  • B. Dubrulle
  • Guowei He

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Computations
  • Couplings
  • Diffusion
  • Dissipation
  • Dynamics
  • Equations
  • Experimental Data
  • Fluid Mechanics
  • Mechanical Properties
  • Navier Stokes Equations
  • Physical Properties
  • Physical Theories
  • Statistics
  • Stratified Fluids
  • Turbulence
  • Turbulent Mixing
  • Two Dimensional

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Calculus or Mathematical Analysis
  • Statistical inference.