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 γ of the small-scale dynamo and the turbulent velocity u rms with shear rate S that are independent of the magnetic Prandtl number: γ ∝ |S| and u rms ∝ |S| 2/3 . For large fluid and magnetic Reynolds numbers, γ, 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, γ ∝ |S| 2/3 , arising solely from the induction equation for a given velocity field.

A jet-driven dynamo (JEDD) from jets-inflated bubbles in cooling flows

“…Comparing equations (1) and (2) we see that this condition is met in the case of turbulence produced by jetinflated bubbles. Singh et al (2017) confirmed the finding of Kolokolov et al (2011) that the linear shear increases the small-scale dynamo growth rate. In their simulation Singh et al (2017) find that the fluctuating magnetic field growth rate increase as γ ∝ |S|.…”

“…Singh et al (2017) confirmed the finding of Kolokolov et al (2011) that the linear shear increases the small-scale dynamo growth rate. In their simulation Singh et al (2017) find that the fluctuating magnetic field growth rate increase as γ ∝ |S|. For S L = 0.009c s k f , where c s is the sound speed and k f = 2π/λ f is wave number of the velocity fluctuations of the turbulence, Singh et al (2017) find that the magnetic field reaches equipartition (where the magnetic pressure is about equal to the turbulent pressure) at a time of τ eq ≃ 190(k f u rms ) −1 .…”

“…In this study the earlier results of dynamo excited by propagating jets (Dubois et al 2009;Gaibler et al 2009;Huarte-Espinosa et al 2011a,b), the results of the heating-mixing simulations (e.g., Hillel & Soker 2016, and the new study by Singh et al (2017) of the enhancement of small-scale turbulent dynamo by large-scale shear, are put together into a coherent picture of what I term a jet-driven dynamo (JEDD) that takes place as part of the JFM in cooling flows, and possibly in other environments where the JFM occurs.…”

“…The derivation presented here is based on the recent analytical and numerical study of Singh et al (2017), where more details and earlier references can be found. The case presented here is that of a turbulence produced by the shear.…”

“…In their simulation Singh et al (2017) find that the fluctuating magnetic field growth rate increase as γ ∝ |S|. For S L = 0.009c s k f , where c s is the sound speed and k f = 2π/λ f is wave number of the velocity fluctuations of the turbulence, Singh et al (2017) find that the magnetic field reaches equipartition (where the magnetic pressure is about equal to the turbulent pressure) at a time of τ eq ≃ 190(k f u rms ) −1 . For λ f ≈ 5 kpc and c s ≈ 800 km s −1 , the shear in the present study (according to equation 1) is S L = 0.07c s k f .…”