Kazantsev dynamo in turbulent compressible flows

TL;DR

This paper investigates the Kazantsev dynamo mechanism in turbulent flows with varying degrees of compressibility and different scaling behaviors, revealing how these factors influence magnetic field growth rates and critical conditions.

Contribution

It generalizes the Kazantsev model to include compressible flows with solenoidal and potential components, analyzing their impact on dynamo action and growth rates.

Findings

Increased compressibility generally decreases the dynamo growth rate.

Different scaling exponents for flow components affect the critical magnetic Reynolds number.

Special behavior observed in three-dimensional flows with respect to the critical scaling exponent.

Abstract

We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model is a generalization of the well-studied Kazantsev model. If both the solenoidal and potential parts have the same scaling exponent, then, as the compressibility of the flow increases, the growth rate decreases but remains positive. If the scaling exponents for the solenoidal and potential parts differ, in particular if they correspond to typical Kolmogorov and Burgers values, we again find that an increase in compressibility slows down the growth rate but does not turn it off. The slow down is, however, weaker and the critical magnetic Reynolds number is lower than when both the solenoidal and potential components display the Kolmogorov scaling. Intriguingly, we find that there exist cases, when the potential part is smoother than the solenoidal part, for which an increase in compressibility increases the growth rate. We also find that the critical value of the scaling exponent above which a dynamo is seen is unity irrespective of the compressibility. Finally, we realize that the dimension $d = 3$ is special, since for all other values of $d$ the critical exponent is higher and depends on the compressibility.