| dc.description.abstract | I report the results of numerical studies of 2-dimensional fully compressible convection
of a fluid in which the dependence of the radiative conductivity on temperature
T is taken as K, (V + aT -5)1 so that central regions of the layer are unstable to convection
whereas the surrounding layers are stable. Calculations have been undertaken
for Rayleigh numbers at the centre of the unstable layer Rc,, = 4.78 106 -9-56 107
and Prandtl numbers a=0.05 - 1. The main result found is that in a (statistically)
stationary state the viscous dissipation decreases with decreasing Prandtl number,
and that the equilibrium of the whole layer is governed by a substantial penetrative
region in which the convective flux is negative. The results found here suggest that
the so called "Roxburgh criterion" can be used to give a good estimate of convective
penetration at small Prandtl numbers.
I also report the results of three sets of numerical experiments involving the interaction
of magnetic fields with 2-dimensional fully compressible convection, were the
fluid has the same conductivity. For these experiments R9subscript cen)= 4.78 106 and [sigma]=1.0,
typically. For one set of experiments a simple model of the evolution of a toroidal flux
tube is considered. The purpose of these numerical experiments was to test the role
played by magnetic buoyancy in the rise of the magnetic flux tube. It was found that
magnetic buoyancy was not important, except possibly when the initial field strength
was large (Chandrasekhar number Q= 10'). In another set of numerical experiments
the initial magnetic field was an uniform horizontal field. One of the results found
was that the magnetic field did not significantly reduce convective penetration, even
when the total (integrated) magnetic energy was of the same order as the total kinetic
energy. The general behaviour found was that magnetic field was expelled from the
convective region, until Q- 10'. Then the initial field strength was strong enough
to suppress convection completely. No oscillatory solutions were found. Finally experiments
were made for initially vertical magnetic fields. An oscillatory solution is
presented.
Also reported are preliminary calculations of 2-dimensional penetrative convection,
for a model were the effects of energy generation and self gravity are included. | en_US |
