Finiterate turbulent diffusion
Abstract
A diffusion model is developed where impurity particles diffuse by moving with infinite velocities, and the directions of these velocities vary discontinuously with infinitely high frequency. The model is applicable to molecular diffusion in gases. In a turbulent flow the velocity's fluctuating component, defining the velocity of the particles in turbulent diffusion, is generally much smaller than the mean transport velocity. Thus the derived equation does not always give physically valid results, such as for the limits of impurity dispersion in a turbulent flow. It is thus assumed that the particle coordinate, i.e., a threedimensional Markovian quantity, is more effective in the case of molecular diffusion in gases than for turbulent diffusion. Instead, the aggregate of the particle coordinates and displacement velocities may be taken as the Markovian random quantity; such quantities describe a sixdimensional random process. By assuming the velocity at each point of the flow has a finite number of values, a meaningful result is yielded. This is used in deriving the socalled equation of diffusion with finite velocity in onedimensional space.
 Publication:

Fluid Mechanics Soviet Research
 Pub Date:
 February 1977
 Bibcode:
 1977FlMSR...6...32G
 Keywords:

 Diffusion Theory;
 Flow Velocity;
 Gaseous Diffusion;
 Molecular Diffusion;
 Particle Diffusion;
 Turbulent Diffusion;
 Channel Flow;
 Equations Of Motion;
 Markov Processes;
 Mathematical Models;
 Particle Motion;
 Three Dimensional Motion;
 Turbulent Flow;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer