Advection by Compressible Turbulent Flows: Renormalization Group Study of Vector and Tracer Admixture
Abstract
Advectiondiffusion problems of magnetic field and tracer field are analyzed using the field theoretic perturbative renormalization group. Both advected fields are considered to be passive, i.e., without any influence on the turbulent environment, and advecting velocity field is generated by compressible version of stochastic NavierStokes equation. The model is considered in the vicinity of space dimension $d=4$ and is a continuation of previous work [N.V. Antonov et al., Phys. Rev. E 95, 033120 (2017)]. The perturbation theory near the special dimension $d=4$ is constructed within a double expansion scheme in $y$ (which describes scaling behavior of the random force that enters a stochastic equation for the velocity field) and $\epsilon=4d$. We show that up to oneloop approximation both types of advected fields exhibit similar universal scaling behavior. In particular, we demonstrate this statement on the inertial range asymptotic behavior of the correlation functions of advected fields. The critical dimensions of tensor composite operators are calculated in the leading order of $(y,\epsilon)$ expansion.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.08711
 Bibcode:
 2019arXiv190408711A
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Physics  Fluid Dynamics
 EPrint:
 Accepted for publication in Theor. Math. Phys