Dynamos in Rotating Compressible Convection (EPSRC Grant, EP/H006842/1)

Grant Summary

rotating convection

Hydromagnetic dynamo theory describes the regeneration of magnetic fields by the motions of an electrically-conducting fluid. In astrophysics and geophysics, many natural dynamos are driven by convection in a rotating fluid. We carried out numerical simulations of dynamo action in rotating compressible convection (Right: The temperature distribution in a simulation of rotating compressible convection). According to standard mean-field dynamo theory, this system should be capable of producing a large-scale magnetic field. This is due to the fact that the small-scale motions in the fluid should produce a significant "alpha-effect", which is the key process that drives large-scale magnetic field generation in simplified mean-field dynamo models. However, regardless of the rotation rate, or the level of thermal stratification within the domain, no significant alpha-effect was measured, and these numerical simulations always produced a small-scale, disordered magnetic field distribution, with no dominant large-scale component. Previous measurements of the alpha-effect in systems of this type have produced contradictory results, depending upon the method of measurement that is used. We believe that we have identified the reason for this discrepancy: the (so called) "test-field method" would tend to over-estimate the alpha-effect because it artificially increases the level of correlation between the mean magnetic field and the mean electromotive force that is induced by the small-scale motions. The absence of an alpha-effect in this system is surprising, and calls into the question the applicability of mean-field theory to dynamo models of this type.

Even though we found no evidence for large-scale dynamo action, the small-scale dynamo that is observed is of interest in its own right. Some care is needed when comparing simulations with different rotation rates because convective motions tend to be less vigorous at higher rotation rates. However, although rotation is not necessary for dynamo action, we have concluded that rotation is generally beneficial for the small-scale dynamo process. On the other hand, variations in the thermal stratification within a rotating convective layer do not seem to have a major effect upon the small-scale dynamo. In dynamos of this type, the magnetic energy stops growing when the magnetic field becomes strong enough locally to impede the stretching due to the flow. We have investigated this process in some detail. In turbulent convection, all of the dynamos that we have studied equilibrate after only a small fraction of the kinetic energy of the flow has been converted into magnetic energy. However, in a weakly-convecting, rapidly-rotating calculation, the magnetic field actually enhances the convective motions and the dynamo eventually reaches at a level at which the magnetic energy actually exceeds the kinetic energy of the flow.

In a very wide domain, the characteristic "granular" pattern in non-rotating convection is organised on a larger (and clearly defined) "mesogranular" scale. Mesogranules enhance the dynamo by increasing the rate at which the magnetic energy grows. Furthermore, localised regions of vertical magnetic flux tend to form at the boundaries of the mesogranules. A similar magnetic field distribution is observed at the surface of the Sun. Intriguingly, mesogranules appear to be absent in rotating compressible convection.

Relevant Publications

Favier, B. & Bushby, P.J., "On the problem of large-scale magnetic field generation in rotating compressible convection" (2013), Journal of Fluid Mechanics, Volume 723, pp. 529-555  ADS

Favier, B. & Bushby, P.J., "Small-scale dynamo action in rotating compressible convection" (2012), Journal of Fluid Mechanics, Volume 690, pp. 262-287  ADS

Bushby P.J., Favier, B., Proctor M.R.E. & Weiss, N.O., "Convectively-driven dynamo action in the quiet Sun" (2012), Geophysical and Astrophysical Fluid Dynamics, Volume 106, pp. 508-523   ADS

B. Favier & P.J. Bushby, Dynamos in rotating compressible convection (2011), Journal of Physics Conference Series, Vol. 318, 072027  Online article

Bushby P.J., Proctor, M.R.E & Weiss, N.O, The influence of stratification upon small-scale convectively-driven dynamos (2011), Proceedings of IAU Symposium 271, "Astrophysical Dynamics: from stars to galaxies" (Nice), Eds. N.H. Brummell, A.S. Brun, M.S. Miesch, Y. Ponty, pp. 197-204  ADS