The connection between the equatorial temperature bias and north–south helicity segregation in numerical simulations of the geodynamo

Abstract

SUMMARY In recent numerical simulations of the geodynamo the dynamo action is driven, primarily, by the effects of helicity, with differential rotation playing only a secondary role. These dynamos display a number of robust features, such as: (i) thin convective columns outside the tangent cylinder whose azimuthally averaged helicity, $\langle h \rangle = \langle {{{\bf u}} \cdot \nabla \times {{\bf u}}} \rangle $, is left-handed in the north and right-handed in the south, (ii) approximately 2-D motion in the equatorial regions, with negligible axial velocity,$\langle {{u}_z} \rangle \approx 0$, (iii) positive radial current at mid-latitudes and negative radial current in the equatorial regions, (iv) a radial outflow in the equatorial regions and (v) elevated temperatures near the equator. We seek the relationship between all five of these observations. First, we note that $\langle {{u}_z} \rangle \approx 0$ near the equator follows from the skew-symmetric distribution of helicity, while a negative radial current at the equator is a generic feature of helicity-driven dynamos which have positive (negative) helicity in the south (north). Next, we confirm an earlier suggestion that the equatorial outflow is driven by Lorentz forces associated with the negative radial current. Crucially, however, this outflow does not account for the elevated equatorial temperatures. Rather, the high temperature near the equator is primarily a consequence of anisotropic turbulent diffusion, which preferentially carries heat radially outward along the equator, this anisotropy being a consequence of the (approximately) 2-D flow near the equator. In short, we show that the high equatorial temperatures are a direct consequence of the skew-symmetric distribution of helicity. Finally, we recall that the high equatorial temperatures can themselves explain the observed helicity distribution, as buoyant anomalies near the equator trigger inertial waves which carry negative helicity upward and positive helicity downward. Thus, there is a direct, two-way coupling between the high equatorial temperatures and the helicity distribution.