Persistence in advection of a passive scalar
Abstract
We consider the persistence phenomenon in advected passive scalar equation in one dimension. The velocity field is random with the ⟨v(k,ω)v(-k,-ω)⟩∼∣k∣-(2+α) . In the presence of the nonlinearity the complete Green’s function becomes G-1=-iω+Dk2+Σ . We determine Σ self-consistently from the correlation function which gives Σ∼kβ , with β=(1-α)/2 . The effect of the nonlinear term in the equation in the O(γ2) is to replace the diffusion term due to molecular viscosity by an effective term of the form Σ0kβ . The stationary correlator for this system is [sech(T/2)]1/β . Using the self-consistent theory we have determined the relation between β and α . Finally, the independent interval approximation (IIA) method is used to determine the persistent exponent.
- Publication:
-
Physical Review E
- Pub Date:
- March 2009
- DOI:
- 10.1103/PhysRevE.79.031112
- arXiv:
- arXiv:0810.0512
- Bibcode:
- 2009PhRvE..79c1112C
- Keywords:
-
- 05.20.Jj;
- 47.27.tb;
- 05.40.-a;
- Statistical mechanics of classical fluids;
- Turbulent diffusion;
- Fluctuation phenomena random processes noise and Brownian motion;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 4 pages