Dynamos in rotating compressible convection
Lead Research Organisation:
Newcastle University
Department Name: Mathematics and Statistics
Abstract
Hydromagnetic dynamo theory describes the regeneration of magnetic fields as the result of the motions of an electrically-conducting fluid. There are many physical examples of dynamos, particularly in geophysics and astrophysics, and dynamo action has been found in recent liquid metal laboratory experiments. Thermal convection is responsible for driving many of these natural dynamos, the vast majority of which also depend upon the dynamical influence of rotation. Most previous studies of dynamo action in rotating convection have adopted the Boussinesq approximation, which means (amongst other things) that the effects of stratification are ignored. By carrying out a series of numerical simulations, we propose to investigate dynamo action in rotating compressible convection, focusing particularly upon the effects that stratification has upon convectively-driven dynamos. Specifically, we shall address the question of whether or not dynamo action in highly-supercritical compressible convection can lead to the formation of large-scale magnetic fields (something that equivalent Boussinesq dynamos fail to do). We shall also establish whether there is an optimal rotation rate and an optimal level of stratification for dynamo action in the weakly-supercritical parameter regime (close to the onset of convective instabilities). Finally, motivated by previous results from Boussinesq convection, we will look for dynamo action in the subcritical parameter regime, i.e. a region of parameter space in which no convective instabilities would occur in the absence of a magnetic field.
Organisations
Publications
Bushby P
(2012)
Convectively driven dynamo action in the quiet Sun
in Geophysical & Astrophysical Fluid Dynamics
Bushby P
(2011)
The influence of stratification upon small-scale convectively-driven dynamos
in Proceedings of the International Astronomical Union
Favier B
(2011)
Small-scale dynamo action in rotating compressible convection
in Journal of Fluid Mechanics
Favier B
(2013)
On the problem of large-scale magnetic field generation in rotating compressible convection
in Journal of Fluid Mechanics
Favier B
(2011)
Dynamos in rotating compressible convection
in Journal of Physics: Conference Series
Favier B
(2011)
Small-scale dynamo action in rotating compressible convection
| Description | 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. 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 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. |
| Exploitation Route | The most obvious beneficiaries from this research will be other researchers (primarily applied mathematicians and physicists) in the field of dynamo theory. Researchers from the solar dynamo and geodynamo communities, in particular, base many of their theoretical models upon mean-field theory. Given that we have shown that this model of dynamo action in rotating compressible convection does not behave according to the predictions of mean-field theory, this calls into question the applicability of this theory to any astrophysical dynamos that are driven by rotationally-influenced convective motions (which is certainly true of the geodynamo and, probably, the solar dynamo as well). This suggests that some of these models mays require a certain degree of revision. Furthermore, we have shown that some care is needed when measuring the mean-field parameters in numerical simulations - the results obtained can be highly dependent upon the measurement technique that is used. Having explained the probable reason for some of the different results that have previously been obtained in this area, we hope to reduce future discrepancies in measurements of this type. Some of our results on dynamo action in non-rotating convection in very large (mesogranular-scale) domains will be of interest to the solar physics community. In particular, we hope that our results will contribute towards our theoretical understanding of the ever-increasing body of observational data that is continuously being produced by the latest generation of telescopes. |
| Sectors | Other |
| URL | http://www.staff.ncl.ac.uk/paul.bushby/EPSRCrotatingdyn.html |