Kazantsev model in non-helical 2.5-dimensional flows

Abstract

We study the dynamo instability for a Kazantsev–Kraichnan flow with three velocity components that depend only on two dimensions $\boldsymbol{u}=(u(x,y,t),v(x,y,t),w(x,y,t))$ often referred to as 2.5-dimensional (2.5-D) flow. Within the Kazantsev–Kraichnan framework 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 cases. 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.