Enhancement of small-scale turbulent dynamo by large-scale shear

Abstract

Small-scale dynamos are ubiquitous in a broad range of turbulent flows with large-scale shear, ranging from solar and galactic magnetism to accretion disks, cosmology and structure formation. Using high-resolution direct numerical simulations we show that in non-helically forced turbulence with zero mean magnetic field, large-scale shear supports small-scale dynamo action, i.e., the dynamo growth rate increases with shear and shear enhances or even produces turbulence, which, in turn, further increases the dynamo growth rate. When the production rates of turbulent kinetic energy due to shear and forcing are comparable, we find scalings for the growth rate $\gamma$ of the small-scale dynamo and the turbulent velocity $u_{\mathrm{rms}}$ with shear rate $S$ that are independent of the magnetic Prandtl number: $\gamma \propto |S|$ and $u_{\mathrm{rms}}\propto |S{|}^{2/3}$. For large fluid and magnetic Reynolds numbers, $\gamma$, normalized by its shear-free value, depends only on shear. Having compensated for shear-induced effects on turbulent velocity, we find that the normalized growth rate of the small-scale dynamo exhibits the scaling, $\tilde{\gamma }\propto |S{|}^{2/3}$, arising solely from the induction equation for a given velocity field.

Improved version submitted to the Astrophysical Journal Letters, 6 pages, 5 figures

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• A new constraint on mean-field galactic dynamo theory
• On the shear-current effect: toward understanding why theories and simulations have mutually and separately conflicted
• Generation of large-scale magnetic fields due to fluctuating $\alpha$ in shearing systems
• Small-scale and large-scale dynamos in global convection simulations of solar-like stars
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• A jet-driven dynamo (JEDD) from jets-inflated bubbles in cooling flows
• Large $\mathrm{Pm}$ small-scale kinematic dynamo in protoneutron stars