Long-time tail effect of the velocity correlation on diffusion-controlled reactions

1997 ◽  
Vol 107 (23) ◽  
pp. 9890-9893 ◽  
Author(s):  
W. Dong
Keyword(s):  
Velocity Correlation ◽  
Diffusion Controlled ◽  
Long Time

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.

THOMPSON's METHOD APPLIED TO THE BROWNIAN AND NON-BROWNIAN DIFFUSION-CONTROLLED REACTIONS OF TYPE kA → lA (l < k)

2002 ◽  
Vol 16 (17) ◽  
pp. 601-613 ◽  
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Renormalization Group ◽  
Good Description ◽  
Wave Length ◽  
Group Scheme ◽  
Single Species ◽  
Critical Dimension ◽  
Stationary Regime ◽  
Brownian Diffusion ◽  
Diffusion Controlled ◽  
Long Time

The diffusion-controlled reactions of type kA → lA, with l < k, including the case of the annihilation reaction kA → 0, are studied by using Thompson's method, both in the case of Brownian (γ = 2) as in the case of anomalous (γ ≠ 2) diffusion conditions. These reactions are known to be strongly dependent on fluctuations below some critical dimension dc. We find dc = γ/(k-1) and the asymptotic behavior of density [Formula: see text]. At d = dc, the density goes as <∊> ~ ( ln t/t)1/k-1. For γ = 2, the scaling results obtained here are in agreement with the renormalization group calculations of Lee15 and a more recent work of Oliveira.8 We go further by also studying the case of an external homogeneous source (h) of single species particles A in the case of the stationary regime. Then we obtain the critical exponent δ in [Formula: see text], the dynamical exponent for the relaxation time Δ′ in (τh ~ hΔ′) and the exponent for the concentration decay ξ in (∊ ~ τ- ξ), with all these quantities evaluated in the limit h → 0. We get relations of scaling among critical indexes, and, in the special case of γ = 2, we recover those results previously obtained by Rácz.30 Thompson's method is a simple alternative way to the renormalization group scheme and has been shown to be a good description for the long-time (long wave-length) regime.

scholarly journals Lagrangian Velocity Correlations and Absolute Dispersion in the Midlatitude Troposphere

2005 ◽  
Vol 62 (10) ◽  
pp. 3831-3836 ◽  
Author(s):  
Jai Sukhatme
Keyword(s):  
Time Scales ◽  
Rossby Waves ◽  
Zonal Flow ◽  
Velocity Correlation ◽  
Planetary Scale ◽  
Time Correlations ◽  
Lagrangian Velocity ◽  
Long Time ◽  
Intermediate Time ◽  
Velocity Correlation Functions

Abstract Employing daily wind data from the ECMWF, passive particle advection is performed to estimate the Lagrangian velocity correlation functions (LVCF) associated with the midlatitude tropospheric flow. In particular, the velocity field is decomposed into time mean and transient (or eddy) components to better understand the nature of the LVCFs. A closely related quantity, the absolute dispersion (AD), is also examined. Given the anisotropy of the flow, meridional and zonal characteristics are considered separately. The zonal LVCF is seen to be nonexponential. In fact, for intermediate time scales it can either be interpreted as a power law of the form τ−α with 0 &lt; α &lt; 1 or as the sum of exponentials with differing time scales—both interpretations being equivalent. More importantly the long time correlations in the zonal flow result in a superdiffusive zonal AD regime. On the other hand, the meridional LVCF decays rapidly to zero. Before approaching zero the meridional LVCF shows a region of negative correlation—a consequence of the presence of planetary-scale Rossby waves. As a result the meridional AD, apart from showing the classical asymptotic ballistic and diffusive regimes, displays transient subdiffusive behavior.

On non-self-similar regimes in homogeneous isotropic turbulence decay

2012 ◽  
Vol 711 ◽  
pp. 364-393 ◽  
Author(s):  
Marcello Meldi ◽  
Pierre Sagaut
Keyword(s):  
Energy Spectrum ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Self Similarity ◽  
Velocity Correlation ◽  
Turbulence Decay ◽  
Long Time ◽  
Self Similar ◽  
Decay Exponent

AbstractBoth theoretical analysis and eddy-damped quasi-normal Markovian (EDQNM) simulations are carried out to investigate the different decay regimes of an initially non-self-similar isotropic turbulence. Breakdown of self-similarity is due to the consideration of a composite three-range energy spectrum, with two different slopes at scales larger than the integral length scale. It is shown that, depending on the initial conditions, the solution can bifurcate towards a true self-similar decay regime, or sustain a non-self-similar state over an arbitrarily long time. It is observed that these non-self-similar regimes cannot be detected, restricting the observation to time exponents of global quantities such as kinetic energy or dissipation. The actual reason is that the decay is controlled by large scales close to the energy spectrum peak. This theoretical prediction is assessed by a detailed analysis of triadic energy transfers, which show that the largest scales have a negligible impact on the total transfers. Therefore, it is concluded that details of the energy spectrum near the peak, which may be related to the turbulence production mechanisms, are important. Since these mechanisms are certainly not universal, this may at least partially explain the significant discrepancies that exist between experimental data and theoretical predictions. Another conclusion is that classical self-similarity theories, which connect the asymptotic behaviour of either the energy spectrum $E(k\ensuremath{\rightarrow} 0)$ or the velocity correlation function $f(r\ensuremath{\rightarrow} + \infty )$ and the turbulence decay exponent, are not particularly relevant when the large-scale spectrum shape exhibits more than one range.

Long-time behavior of the diffusion-controlled A+B→0 reaction with hopping energy relaxation

1997 ◽  
Vol 106 (8) ◽  
pp. 3157-3158
Author(s):  
S. D. Baranovskii ◽  
F. Hensel ◽  
J. E. Golub ◽  
P. Thomas
Keyword(s):  
Energy Relaxation ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Diffusion Controlled ◽  
Long Time ◽  
Hopping Energy

A+B→0 ENHANCED DIFFUSION-CONTROLLED REACTIONS UNDER STATIONARY REGIME CONDITION THROUGH THOMPSON'S APPROACH

2004 ◽  
Vol 18 (09) ◽  
pp. 345-353
Author(s):  
CLÁUDIO NASSIF ◽  
P. R. SILVA
Keyword(s):  
Good Description ◽  
Group Scheme ◽  
Stationary Regime ◽  
Brownian Diffusion ◽  
Zero Field ◽  
Enhanced Diffusion ◽  
Diffusion Controlled ◽  
Simple Alternative ◽  
Time Regime ◽  
Long Time

In this work, Thompson's method is used to study the A+B→0 reactions controlled by anomalous and brownian diffusion in the case of an external homogeneous source (h) of particles A and B under sthequiometric condition (the same input rate h) and also in the special case of the stationary regime. So the novelty in the present work is that we are able to obtain for such kind of reactions (σ=1) the static critical exponent δ of concentration [Formula: see text], the dynamical exponent for the relaxation time Δ'(τh~h-Δ') and the exponent for the concentration decaying ξ(∊~τ-ξ), with all these quantities evaluated in the limit h→0 (zero-field-rate). We also get scaling relations among new critical indexes. After we go further by obtaining more general results for such exponents so that we are able to include also the case of A+A→0(A) reactions within an unified scheme as already made before by introducing a general effective action (Aσ,γ). Thus, when we consider the case σ=0 (A,+A→0(A) reactions) we recover those critical exponents (δ,Δ',ξ) for anomalous coalescence reactions of type kA→lA(l<k). And when we even make γ=2 (brownian diffusion) we get the exponents previously given by Rácz, and also some results obtained by Lee and Oliveira. Thompson's method is a simple alternative way to the renormalization group scheme and has been shown to be a good description for long-time regime.

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