Helicity flux in a shear flow turbulence

Run similar to Run A of Brandenburg (2018), but the density changes from 1 at z = 0 to about 0.002 at z = π/2. Butterfly diagram is similar to before; see Figure ??. The frequency is now ω ≈ 6.6 η_{t0}k_{1}^{2} instead of 1.16 η_{t0}k_{1}^{2} in the unstratified case. This is very surprising.

        Figure 1: ppbutter_Strat288a

The small-scale magnetic helicty has now the same sign as the large-scale magnetic helicty; see the blue line in Figure ?? compared with \overline{A}·\overline{B} (red line). The total \overline{A · B} is shown in red.

The second panel of Figure ?? shows at z > π/4, \overline{ω · ρu} (green) is almost as large as \overline{j · b}. The upper part is fully quenched, it seems, but the cycle still proceeds, with an even higher frequency. The smallscale magnetic helicity flux is also of the wrong sign (positive); see panels 3 and 4.

References

Brandenburg, A. 2018, Astron. Nachr., 339, 631 640Magnetic helicity and fluxes in an inhomogeneous α^{2} dynamo

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                                                    Figure 2: pphelflux_Strat288a

Figure 3: pphelflux_Om2kf60a, k_{f} = 60.  Figure 4: pphelflux_hel_b0_Lz2b2

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