ISSN:
1572-9613
Keywords:
Turbulent diffusion
;
shear layers
;
long-range correlations
;
renormalization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract Recently, a rigorous renormalization theory for various scalar statistics has been developed for special modes of random advection diffusion involving random shear layer velocity fields with long-range spatiotemporal correlations. New random shearing direction models for isotropic turbulent diffusion are introduced here. In these models the velocity field has the spatial second-order statistics of an arbitrary prescribed stationary incompressible isotropic random field including long-range spatial correlations with infrared divergence, but the temporal correlations have finite range. The explicit theory of renormalization for the mean and second-order statistics is developed here. With ε the spectral parameter, for −∞〈ε〈4 and measuring the strength of the infrared divergence of the spatial spectrum, the scalar mean statistics rigorously exhibit a phase transition from mean-field behavior for ε〈2 to anomalous behavior for ε with 2〈ε〈4 as conjectured earlier by Avellaneda and the author. The universal inertial range renormalization for the second-order scalar statistics exhibits a phase transition from a covariance with a Gaussian functional form for ε with ε〈2 to an explicit family with a non-Gaussian covariance for ε with 2〈ε〈4. These non-Gaussian distributions have tails that are broader than Gaussian as ε varies with 2〈ε〈4 and behave for large values like exp(−C c |x|4−ε), withC c an explicit constant. Also, here the attractive general principle is formulated and proved that every steady, stationary, zero-mean, isotropic, incompressible Gaussian random velocity field is well approximated by a suitable superposition of random shear layers.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02186761
Permalink
