Dispersion by random velocity fields

1975 ◽  
Vol 67 (1) ◽  
pp. 145-153 ◽  
Author(s):  
R. Phythian
Keyword(s):  
Correlation Function ◽  
Velocity Field ◽  
Velocity Fields ◽  
Random Motion ◽  
Velocity Correlation ◽  
Spectral Functions ◽  
Velocity Correlation Function ◽  
Lagrangian Velocity ◽  
Computer Calculations ◽  
Exact Computer

A simple approximation is proposed for the problem of the dispersion of marked particles in an incompressible fluid in random motion when the probability distribution of the velocity field is taken as Gaussian, homogeneous, isotropic, stationary and of zero mean. Approximations for the Lagrangian velocity correlation function and the dispersion are given and compared with exact computer calculations of Kraichnan. Agreement is found to be good except for time-independent velocity fields and singular wavenumber spectral functions.

The effective long-time diffusivity for a passive scalar in a Gaussian model fluid flow

1978 ◽  
Vol 89 (2) ◽  
pp. 241-250 ◽  
Author(s):  
R. Phythian ◽  
W. D. Curtis
Keyword(s):  
Diffusion Processes ◽  
Fluid Velocity ◽  
Gaussian Model ◽  
Effective Diffusivity ◽  
Passive Scalar ◽  
Random Motion ◽  
Velocity Correlation ◽  
Molecular Diffusivity ◽  
Velocity Correlation Function ◽  
Long Time

The problem considered is the diffusion of a passive scalar in a ‘fluid’ in random motion when the fluid velocity field is Gaussian and statistically homogeneous, isotropic and stationary. A self-consistent expansion for the effective long-time diffusivity is obtained and the approximations derived from this series by retaining up to three terms are explicitly calculated for simple idealized forms of the velocity correlation function for which numerical simulations are available for comparison for zero molecular diffusivity. The dependence of the effective diffusivity on the molecular diffusivity is determined within this idealization. The results support Saffman's contention that the molecular and turbulent diffusion processes interfere destructively, in the sense that the total effective diffusivity about a fixed point is less than that which would be obtained if the two diffusion processes acted independently.

Negative tails in the velocity correlation function of supercooled liquids

2003 ◽  
Vol 119 (18) ◽  
pp. 9661-9666 ◽  
Author(s):  
Alberto De Santis ◽  
Alessandro Ercoli ◽  
Dario Rocca
Keyword(s):  
Correlation Function ◽  
Supercooled Liquids ◽  
Velocity Correlation ◽  
Velocity Correlation Function
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