References for Discussions: | References for Lectures:

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
Hereis a link to a general review article on the MRI. Hereand 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

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
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:

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