{"title":"On the theory of convection in the Earth’s core","authors":"S. Braginsky, P. Roberts","doi":"10.1201/9780203493137-3","DOIUrl":"https://doi.org/10.1201/9780203493137-3","url":null,"abstract":"","PeriodicalId":205860,"journal":{"name":"Advances in Nonlinear Dynamos","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128856007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Thin aspect ratio αΩ-dynamos in galactic discs and stellar shells","authors":"A. Soward","doi":"10.1201/9780203493137-8","DOIUrl":"https://doi.org/10.1201/9780203493137-8","url":null,"abstract":"","PeriodicalId":205860,"journal":{"name":"Advances in Nonlinear Dynamos","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125573610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2003-04-24DOI: 10.1201/9780203493137.CH1
P. Hoyng
{"title":"The field, the mean and the meaning","authors":"P. Hoyng","doi":"10.1201/9780203493137.CH1","DOIUrl":"https://doi.org/10.1201/9780203493137.CH1","url":null,"abstract":"","PeriodicalId":205860,"journal":{"name":"Advances in Nonlinear Dynamos","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114939907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2003-04-01DOI: 10.1201/9780203493137.CH10
M. Berger
{"title":"Topological quantities in magnetohydrodynamics","authors":"M. Berger","doi":"10.1201/9780203493137.CH10","DOIUrl":"https://doi.org/10.1201/9780203493137.CH10","url":null,"abstract":"","PeriodicalId":205860,"journal":{"name":"Advances in Nonlinear Dynamos","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116687513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2003-04-01DOI: 10.1201/9780203493137.CH5
M. Schüssler, A. Ferriz-Mas
{"title":"Magnetic flux tubes and the dynamo problem","authors":"M. Schüssler, A. Ferriz-Mas","doi":"10.1201/9780203493137.CH5","DOIUrl":"https://doi.org/10.1201/9780203493137.CH5","url":null,"abstract":"","PeriodicalId":205860,"journal":{"name":"Advances in Nonlinear Dynamos","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131503938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2003-04-01DOI: 10.1201/9780203493137.CH7
K. Julien, E. Knobloch, S. Tobias
Fully nonlinear convection in a strong imposed magnetic field is studied in the regime in which the convective velocities are not strong enough to distort the magnetic field substantially. Motivated by convection in sunspots both vertical and inclined imposed fields are considered. In this regime the leading order nonlinearity is provided by the distortion of the horizontally averaged temperature profile. For overstable convection this profile is determined from the solution of a nonlinear eigenvalue problem for the (time-averaged) Nusselt number and oscillation frequency, and evolves towards an isothermal profile with increasing Rayleigh number. In the presence of variable magnetic Prandtl number ζ(z) the profile is asymmetric with respect to midlevel, but nonetheless develops an isothermal core in the highly supercritical regime. A hysteretic transition between two distinct convection regimes is identified in the inclined case, and used to suggest an explanation for the sharp boundary between the sunspot umbra and penumbra. These results are obtained via an asymptotic expansion in inverse powers of the Chandrasekhar number, and generalize readily to a polytropic atmosphere.
{"title":"Highly supercritical convection in strong magnetic fields","authors":"K. Julien, E. Knobloch, S. Tobias","doi":"10.1201/9780203493137.CH7","DOIUrl":"https://doi.org/10.1201/9780203493137.CH7","url":null,"abstract":"Fully nonlinear convection in a strong imposed magnetic field is studied in the regime in which the convective velocities are not strong enough to distort the magnetic field substantially. Motivated by convection in sunspots both vertical and inclined imposed fields are considered. In this regime the leading order nonlinearity is provided by the distortion of the horizontally averaged temperature profile. For overstable convection this profile is determined from the solution of a nonlinear eigenvalue problem for the (time-averaged) Nusselt number and oscillation frequency, and evolves towards an isothermal profile with increasing Rayleigh number. In the presence of variable magnetic Prandtl number ζ(z) the profile is asymmetric with respect to midlevel, but nonetheless develops an isothermal core in the highly supercritical regime. A hysteretic transition between two distinct convection regimes is identified in the inclined case, and used to suggest an explanation for the sharp boundary between the sunspot umbra and penumbra. These results are obtained via an asymptotic expansion in inverse powers of the Chandrasekhar number, and generalize readily to a polytropic atmosphere.","PeriodicalId":205860,"journal":{"name":"Advances in Nonlinear Dynamos","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123044005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-01-09DOI: 10.1201/9780203493137.ch6
G. Rudiger, R. Arlt
The theory of the solar/stellar activity cycles is presented, based on the mean-field concept in magnetohydrodynamics. A new approach to the formulation of the electromotive force and the theory of differential rotation and meridional circulation is described. Dynamo cycles in the overshoot layer and distributed dynamos are compared, with the latter including the influence of meridional flow. The overshoot layer dynamo reproduces the solar cycle periods and the butterfly diagram only if alpha=0 in the convection zone (CZ). The distributed dynamo including meridional flows shows the observed butterfly diagram even with a positive dynamo-alpha in CZ. The nonlinear feedback of strong magnetic fields on differential rotation leads to grand minima in the cyclic activity similar to those observed. Our 2D model contains the large- and small-scale feedback of magnetic fields on diff. rotation and induction in a mean-field formulation (Lambda-, alpha-quenching). Grand minima may also occur if a dynamo occasionally falls below its critical eigenvalue. We never found any indication that such an on-off dynamo collapses by this effect after being excited. The full quenching of turbulence by strong magnetic fields as reduced induction (alpha) and reduced turbulent diffusivity (eta_T) is studied in 1D. We find a stronger dependence of cycle period on dynamo number compared with a pure alpha-quenching model giving a very weak cycle period dependence. Also the temporal fluctuations of alpha and eta_T from a random-vortex simulation were applied to a dynamo. Then the low `quality' of the solar cycle can be explained with a small number of giant cells as dynamo-active turbulence. The transition from almost regular magnetic oscillations (many vortices) to a more or less chaotic time series (very few vortices) is shown.
{"title":"Physics of the solar cycle","authors":"G. Rudiger, R. Arlt","doi":"10.1201/9780203493137.ch6","DOIUrl":"https://doi.org/10.1201/9780203493137.ch6","url":null,"abstract":"The theory of the solar/stellar activity cycles is presented, based on the mean-field concept in magnetohydrodynamics. A new approach to the formulation of the electromotive force and the theory of differential rotation and meridional circulation is described. Dynamo cycles in the overshoot layer and distributed dynamos are compared, with the latter including the influence of meridional flow. The overshoot layer dynamo reproduces the solar cycle periods and the butterfly diagram only if alpha=0 in the convection zone (CZ). The distributed dynamo including meridional flows shows the observed butterfly diagram even with a positive dynamo-alpha in CZ. The nonlinear feedback of strong magnetic fields on differential rotation leads to grand minima in the cyclic activity similar to those observed. Our 2D model contains the large- and small-scale feedback of magnetic fields on diff. rotation and induction in a mean-field formulation (Lambda-, alpha-quenching). Grand minima may also occur if a dynamo occasionally falls below its critical eigenvalue. We never found any indication that such an on-off dynamo collapses by this effect after being excited. The full quenching of turbulence by strong magnetic fields as reduced induction (alpha) and reduced turbulent diffusivity (eta_T) is studied in 1D. We find a stronger dependence of cycle period on dynamo number compared with a pure alpha-quenching model giving a very weak cycle period dependence. Also the temporal fluctuations of alpha and eta_T from a random-vortex simulation were applied to a dynamo. Then the low `quality' of the solar cycle can be explained with a small number of giant cells as dynamo-active turbulence. The transition from almost regular magnetic oscillations (many vortices) to a more or less chaotic time series (very few vortices) is shown.","PeriodicalId":205860,"journal":{"name":"Advances in Nonlinear Dynamos","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128635015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2001-09-27DOI: 10.1201/9780203493137.ch9
A. Brandenburg
The advantages of high-order finite difference scheme for astrophysical MHD and turbulence simulations are highlighted. A number of one-dimensional test cases are presented ranging from various shock tests to Parker-type wind solutions. Applications to magnetized accretion discs and their associated outflows are discussed. Particular emphasis is placed on the possibility of dynamo action in three-dimensional turbulent convection and shear flows, which is relevant to stars and astrophysical discs. The generation of large scale fields is discussed in terms of an inverse magnetic cascade and the consequences imposed by magnetic helicity conservation are reviewed with particular emphasis on the issue of alpha-quenching.
{"title":"Computational aspects of astrophysical MHD and turbulence","authors":"A. Brandenburg","doi":"10.1201/9780203493137.ch9","DOIUrl":"https://doi.org/10.1201/9780203493137.ch9","url":null,"abstract":"The advantages of high-order finite difference scheme for astrophysical MHD and turbulence simulations are highlighted. A number of one-dimensional test cases are presented ranging from various shock tests to Parker-type wind solutions. Applications to magnetized accretion discs and their associated outflows are discussed. Particular emphasis is placed on the possibility of dynamo action in three-dimensional turbulent convection and shear flows, which is relevant to stars and astrophysical discs. The generation of large scale fields is discussed in terms of an inverse magnetic cascade and the consequences imposed by magnetic helicity conservation are reviewed with particular emphasis on the issue of alpha-quenching.","PeriodicalId":205860,"journal":{"name":"Advances in Nonlinear Dynamos","volume":"210 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123385227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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