TURBULENT "DYNAMO" IN THE PASSIVE SCALAR PROBLEM

Abstract

A turbulent magnetic dynamo can be considered as the evolution of a vector field in a turbulent fluid flow. The problem of evolution of scalar fields (e.g., number density of small particles) in a turbulent fluid flow is similar to the turbulent magnetic dynamo. The dynamo instability results in generation of magnetic field. The most important effect which can cause a generation of mean magnetic field in a turbulent fluid flow is the α-effect: α = − (1/3)〈 τu · (∇ × u)〉, whereuis the turbulent velocity field with the correlation time τ. A similar instability in the passive scalar problem results in formation of large-scale inhomogeneous structures in a spatial distribution of particles due to the β-effect: β= 〈 τ up (∇ · up)〉, whereu p is the random velocity field of the particles which they acquire in a turbulent fluid velocity field. The effect is caused by inertia of particles which results in divergent velocity field of the particles. This results in additional turbulent nondiffusive flux of particles.