References

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=__References for Discussions:__=

These references will be useful for the discussions:
__Transport Coefficient Discussion:__ Here is the [|link] to a paper on the difficulties of determining the alpha-effect at high Rm for a family of 2.5D flows. Here is a [|paper] by Leprovost and Kim, which investigates the effect of shear and magnetic field on dynamo quenching and momentum transport reduction. Results for 3-D homogeneous turbulence and the Galloway-Proctor flow using the test-field method can be found [|here].

__Magnetostrophic Turbulence Discussion:__ Here is a paper [|"Magnetostrophic Turbulence and the Geodynamo"] which has appeared in the Proceedings of the IUTAM Symposium on Turbulence held in Nagoya, Japan, 2006. Some analysis of the linear dispersion relation for magnetostrophic convection is available [|here] These are two recent reviews on the related problem of zonal flows in plasma.The [|first] is more detailed.The [|second] is an update on the first, and has more material on experiments. These three papers present work on resistivity gradient driven turbulence (RGDT), a type of low Rm resistive MHD wave turbulence relevant to collisional magnetized plasmas.This is of potential relevance to magnetostrophic turbulence, in that both are systems which evolve by advection and for which the advected field is linearly related to the advecting velocity.In contrast to magnetostrophic turbulence in the geodynamo, RGDT is wave turbulence at lower effective Peclet number,albeit in more complicated geometry.[|RGDT.pdf], [|RGDT Spectrum.pdf], [|RGDT-Impurities.pdf]

Some papers on shell models of (non-magnetostrophic!) turbulence: [|magnetohydrodynamic turbulence] (Plunian & Stepanov, 2007), [|rotating turbulence] (Hattori et al., 2004); [|thermal convective turbulence] (Mingshun & Shida, 1997).

This paper (Gubbins, Masters & Nimmo, 2008) [|f_cr.pdf] is not directly related to MHD turbulence but proposes a new layer around the inner core boundary that to some extent replaces the conventional mushy layer; it seems to contradict the idea of blobs rising from a predominantly solid mushy zone in the inner core.

__Alignment Cross-Helicity Discussion__ Here are some links to papers on the Archontis and related dynamos: [|Archontis, Dorch and Nordlund 2007] [|Cameron and Galloway 2006a] [|Cameron and Galloway 2006b] Here is a [|paper] on the theory of Dynamic Alignment in Driven MHD Turbulence. The following two articles report the results of measurements of the [|alignment angle] and [|energy spectrum] in numerical simulations.

__Magnetorotational Instability and Dynamos Discussion__ [|Here]is a link to a general review article on the MRI. [|Here]and [|here] are two recent papers which address, respectively, numerical convergence of MRI turbulence and how it depends on the diffusivities in the problem. For a paper discussing some of the issues relevant to the saturation of the MRI [|see]. This paper appeared in Stellar Fluid Dynamics and Numerical Simulations; From the Sun to Neutron Stars, M. Rieutord and B. Dubrulle (eds), EAS Publication Series 21, 81--104 (2006).

This is a [|paper] that discusses the mean field magnetohydrodynamics of accretion disks

Two papers that discuss the importance of boundary conditions in global models of the MRI are [|here] and [|here].

__Magnetic helicity

(i)__[| Magnetic Helicity Density and Its Flux in Weakly Inhomogeneous Turbulence] (ii) [|Strong mean field dynamos require supercritical helicity fluxes] (iii) [|Galactic dynamo and helicity losses through fountain flow] (iv) [|Kinetic and magnetic α-effects in non-linear dynamo theory]

__Jets in Jupiter

Geodynamo Reversals__

Various mechanisms for reversals are discussed [|here]

The frequency of geomagnetic excursions and erratic fluctuations in the dipole moment led to the suggestion that the geodynamo is structurally unstable [|(Gubbins & Zhang 2000)]and is possibly stabilised by the inner core [|(Gubbins 1999)]. The most remarkable feature of excursions and reversals is the apparent tendency for poles to track around the Pacific [|(Love 2000)], but this can be explained if magnetic flux remains concentrated around the Pacific during the reversal. A simple kinematic dynamo with equatorial symmetry shows this [|(Gubbins & Sarson 1994)] and explains the distribution of poles for the last reversal satisfactorily [|(Gubbins & Love 1998)]. Similar behaviour has been seen in a 2.5D convective model [|(Sarson & Jones 1999)] but not yet in a 3D model.

A [|short paper] looking at the statistics of observed reversals, and using a toy model to produce similar sequences of reversals.

__Shear Discussion__

__Climate discussion__

Various papers that discuss the past effects of solar variability on climate can be found here [|2007_StagerLake_JGR.pdf], [|2002_RuzFeyn_SolInfNAM_JGR.pdf], [|2004_Ruzetal_TemPattern_GRL.pdf], [|2006_Nile_RuzFeynYung.pdf] and [|2007_Ruz_ClimPatternns_ASR.pdf] A paper showing the importance of including the basic signal and modulation of the solar forcing when inputting into climate models was pubished in 2001 in the Journal of Climate. Paper is available [|here]

__Density-stratification Discussion:__ Here is a paper [|Differential rotation in giant planets maintained by density-stratified turbulence] which is in press with GAFD. Here is a preprint on [|linear theory of rapidly rotating compressible convection]

__Turbulent convection and convective dynamo Discussion:__ Here are a few (recent and less recent) papers that I (Francois) will briefly describe and link together on Thursday in the context of the small-scale dynamo problem (Paul will probably give some more specific references regarding the convective dynamo itself): [|Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence (Yousef, Rincon & Schekochihin 2007)] [|Anisotropy, inhomogeneity and inertial range scalings in turbulent convection (Rincon 2006)] [|Mesoscale flows in large aspect ratio simulations of turbulent compressible convection (Rincon, Lignieres & Rieutord 2005)] [|Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell (Verzicco & Camussi 2003)] [|Scale-by-scale budget and similarity laws for shear turbulence (Casciola et al. 2003)] [|Clustering of Plumes in Turbulent Convection (Parodi et al. 2004)] [|Large Scale Structures in Rayleigh-Bénard Convection at High Rayleigh Numbers (Hartlep, Tilgner & Busse 2003)]

__Scaling Laws in Dynamos Discussion;

Convection, Differential Rotation, Meridional Flows, Stable Layers and Dynamos Discussion:

The Tachocline Discussion:__

A discussion of beta-plane MHD in the tachocline is included [|here] A paper on instabilities in the slow tachocline accepted by Astronomy and Astrophysics [|Tachocline_instability.pdf]

Stuff from Nic Brummell: Papers on magnetic buoyancy instabilities generated by shearing of radial fields: [|Paper1] [|Paper2]

Here are Sacha Brun's contributions on the tachocline and MHD instabilities and dynamo action in stellar radiative zone: [|Zahn, Brun, Mathis A&A 2007] [|Brun & Zahn A&A 2006] [|Brun AN, 2007] Check also papers by: [|Spruit A&A 2002] and by: [|Braithwaite, A&A 2006]

__Dynamos Driven By Instabilities__

The paper by Lara Silvers can be found here: [|Silvers2008]

Here is what Nic Brummell is talking about: [|Tube dynamo paper]

Here are several references related to Francois' contribution to the discussion: [|Subcritical dynamos in shear flows (Rincon, Ogilvie, Proctor & Cossu 2008)] [|Self-sustaining nonlinear dynamo process in Keplerian shear flows (Rincon, Ogilvie & Proctor 2007)] [|On self-sustaining processes in Rayleigh-stable rotating plane Couette flows and subcritical transition to turbulence in accretion disks (Rincon, Ogilvie & Cossu 2007)] [|Visualizing the geometry of state space in plane Couette flow (Gibson, Halcrow & Cvitanović 2008)] [|Exact coherent structures in pipe flow: travelling wave solutions (Wedin & Kerswell 2004)] [|On a self-sustaining process in shear flows (Waleffe 1997)] [|Sustained Magnetoshear Instabilities in the Solar Tachocline (Miesch 2007)] [|On magnetic instabilities and dynamo action in stellar radiation zones (Zahn, Brun & Mathis 2007)] [|Dynamo Action Driven by Shear and Magnetic Buoyancy (Cline, Brummell & Cattaneo 2003)]

__Dynamos at Low Pm__

[|Here] is a discussion of turbulent dynamos with coherent structures and how they can work at low Pm

=__References for Lectures:__=

__Navier Stokes alpha-turbulence:__

This talk is based on [|this paper in press in JFM]. The development addresses issues raised in this paper by [|Holm (2002)] which is based on the orginal paper by [|Andrews & McIntyre (1978)]

__The Rattleback__

The dynamics of the rattleback is described [|here]

__A new approach to turbulence__

An introduction is [|here]