Kazantsev model in nonhelical 2.5D flows

TL;DR

This paper analyzes the dynamo instability in 2.5D flows using the Kazantsev-Kraichnan model, deriving analytical growth rates and spectra, and validating findings with numerical simulations.

Contribution

It provides a novel analytical framework for understanding dynamo behavior in 2.5D flows and highlights non-commuting limits of flow dimensionality and magnetic Reynolds number.

Findings

Analytical growth rates for dynamo instability in 2.5D flows.

Power-law energy spectra of unstable modes differ from 2D and 3D cases.

Good agreement between analytical results and numerical simulations.

Abstract

We study the dynamo instability for a Kazantsev-Kraichnan flow with three velocity components that depends only on two-dimensions u = (u(x, y, t), v(x, y, t), w(x, y, t)) often referred to as 2.5 dimensional (2.5D) flow. Within the Kazantsev-Kraichnan frame- work we derive the governing equations for the second order magnetic field correlation function and examine the growth rate of the dynamo instability as a function of the control parameters of the system. In particular we investigate the dynamo behaviour for large magnetic Reynolds numbers Rm and flows close to being two-dimensional and show that these two limiting procedures do not commute. The energy spectra of the unstable modes are derived analytically and lead to power-law behaviour that differs from the three dimensional and two dimensional case. The results of our analytical calculation are compared with the results of numerical simulations of dynamos driven by prescribed fluctuating flows as well as freely evolving turbulent flows, showing good agreement.