Cellular Dynamo in a RotatingCellular Dynamo in a RotatingSpherical ShellSpherical Shell

Alexander GetlingAlexander GetlingLomonosov Moscow State UniversityLomonosov Moscow State University

Moscow, RussiaMoscow, Russia

Radostin Simitev,Radostin Simitev, Friedrich Busse Friedrich Busse University of Bayreuth, GermanyUniversity of Bayreuth, Germany

The problem of solar The problem of solar dynamo:dynamo: interplay between interplay between

global and local magnetic fields global and local magnetic fields needs to be includedneeds to be included

Mean-field electrodynamics Mean-field electrodynamics →→ no local fieldsno local fields considered considered

Possible alternative Possible alternative →→ “ “deterministic” dynamo deterministic” dynamo with well-with well-defineddefined structural elements in the flow andstructural elements in the flow and magnetic fieldmagnetic field

Kinematic model of Kinematic model of cellular dynamocellular dynamo

(cell = toroidal eddy)(cell = toroidal eddy)::

A.V. Getling and B.A. Tverskoy, A.V. Getling and B.A. Tverskoy,

Geomagn. AeronGeomagn. Aeron. . 1111, 211, 389 , 211, 389

(1971)(1971)

Convective mechanism of Convective mechanism of magnetic-field amplification magnetic-field amplification

and structuring and structuring

This study is based onThis study is based on

numerical simulations of numerical simulations of cellular magnetoconvection in cellular magnetoconvection in

a rotating spherical shella rotating spherical shell

The problemThe problem

Spherical fluid shellSpherical fluid shell Stress-free, electrically insulating Stress-free, electrically insulating

boundaries with perfect heat conductivityboundaries with perfect heat conductivity Uniformly distributed internal heat Uniformly distributed internal heat

sourcessources Boussinesq approximationBoussinesq approximation A small quadratic term is present in theA small quadratic term is present in the

temperaturetemperature dependence of densitydependence of density

The geometry of the The geometry of the problemproblem

Static temperature profileStatic temperature profile

o

i2oi

12

0s

s2

,1

1

2

1

3,

1

2

0

r

rdTTT

c

q

rrT

c

qT

p

p

Physical parameters of the Physical parameters of the problemproblem

The case discussed hereThe case discussed here

Geometrical parameter: Geometrical parameter: ηη = = 00..66

Physical parameters: Physical parameters: RRi i = = 30003000, , RRee = = − −

60006000, , ττ = = 110, 0, PP = = 11, , PPmm==3030

Computational parameter: Computational parameter: mm = = 55

Static profiles of temperatureStatic profiles of temperatureand its gradientand its gradient

Pseudospectral code Pseudospectral code employed:employed:

F.H. F.H. Busse, Busse, E. E. Grote, Grote, and A. and A.

Tilgner,Tilgner, Stud. Geophys. Geod.Stud. Geophys. Geod.

4242, 211 (1998), 211 (1998)

Radial velocity at Radial velocity at rr == rrii ++ 0.50.5 dd

t = 98.73

Azimuthal velocity and Azimuthal velocity and meridional streamlinesmeridional streamlines

t = 98.73

Radial magnetic field at Radial magnetic field at rr == rroo ++

0.70.7 dd

t = 98.73 t = 101.73

Radial magnetic field at Radial magnetic field at rr == rroo

Azimuthal magnetic field and Azimuthal magnetic field and meridional field linesmeridional field lines

t = 95.73 t = 101.73

Variations in poloidal Variations in poloidal components components HH11

00 and and HH2200 at at r r = =

0.50.5

Variations in full magnetic Variations in full magnetic energyenergy

Variations in dipolar-field Variations in dipolar-field energyenergy

axisymm. pol.axisymm. tor.

asymm. pol.asymm. tor.

Thank you for your Thank you for your attentionattention