International Summer Institute for Modeling in Astrophysics

The effects of a uniform horizontal magnetic field on jets dynamics in 2D Boussinesq turbulence, i.e. Howard-Krishnamurti problem are studied with a numerical simulation. For a fixed fluid and magnetic diffusivity, it is shown that as the imposed field strength becomes larger jets start behaving in a more organized way, i.e. achieve stationary state and are finally quenched. The time evolution of total stress, Reynolds stress, Maxwell stress is examined and all the stresses are shown to vanish when jets are quenched. The quenching of jets is confirmed for different values of magnetic diffusivity, albeit the required field strength increases. It is also shown that the inclusion of overstable modes reinforces jets where Maxwell stress overcomes Reynolds stress. For a larger imposed field jets are shown to quench. A possible mechanism for the transition to the reinforcement of jets by Maxwell stress is discussed based on the transition in the most unstable mode in the underlying turbulence.

This project investigates the role of radiation in Rayleigh-Taylor instabilities by performing linear stability analyses of a plane parallel background equilibrium, with a semi-infinite medium 1 overlying a semi-infinite medium 2, in a gravitational field g and a radiation flux F normal to the discontinuity.

Motivated by recent observations of retrograde planets, we investigated the orbital decay of a retrograde planet embedded in a protoplanetary disk. We treated both gravitational and hydrodynamic drag, and found the migration time scale ranges from 10³ to 10⁵ years for planet masses between 10^-3 to 10¹ Jupiter masses. We also found that a highly inclined orbit can increase this time scale by a factor of 10 and that due to inclination damping, the final inclination is unlikely to be greater than 50 degrees.

In this project we address the question of whether a flow that is not a dynamo can be made to exhibit dynamo-like properties by feeding it with a small amount of magnetic field. This may be pertinent to the solar dynamo and the processes that sustain it. We present a 3-D fully nonlinear magnetohydrodynamic simulation of the dynamo properties of a time-dependent ABC flow and discuss a method for leaking magnetic field into the computational domain. Our results suggest that sufficient magnetic feeding significantly boosts the magnetic energy of nondynamo flows and can maintain a mangetic field for long times.

We investigate local radiative hydrodynamic instabilities in the envelopes of massive stars. Two different stellar models are considered, a simple polytropic model and a more realistic stellar evolution code model. For both cases, we compare the local optical depth and radiative flux with analytically derived instability criteria. Only a thin outer shell of the star, containing a mass of about 10^-6 M_star to 10^-5 M_star, can be subjected to this instability. However, the growth rate of the instability is relatively fast (about 10,000s) indicating a possible run-away effect.

The collapse of star-forming molecular clouds depends critically on radiation feedback from embedded protostars. In general, radiative heating raises the local Jeans mass, helping the gas resist fragmentation. However, the strength of this effect should depend on the metallicity of the star-forming region through its effect on the dust opacity, which determines the level of coupling between the matter and the radiation. In this project, we perform a series of AMR radiation-hydrodynamic simulations with the ORION code to determine what effect varying this coupling has on the star formation process.

Thermohaline mixing is the mechanism that governs the photospheric composition of low- and intermediate-mass stars, and explains observations in these stars. It is important to study this instability with the hydrodynamic theory, and to derive prescriptions for the turbulent mixing that can be implemented in stellar codes. In this project, we discuss the formation of salt fingers on stable state, for different perturbations, when we use the small Peclet number approximation. The dominant mode of thermohaline mixing is different from the most unstable mode.

We carry out two-dimensional hydrodynamical simulations to investigate the effects of the turbulence caused by gravitational instability on the migration of a 10 Jupiter-mass planet. We model three discs with different amounts of turbulence and model two scenarios: the first scenario allows the planet to migrate immediately and we find that the migration rates are similar in all three discs, regardless of the amount of turbulence. The second method involves keeping the planet fixed on a circular orbit such that it opens up a gap, before allowing it to migrate. We find that although the gap properties appear to be similar in all three cases, the migration rate is faster in a disc with a lower amount of turbulence.

The project is an extension of the work on f-plane magnetohydrodynamic (MHD) turbulence and its consequences on momentum transport. A somewhat detailed overview is given, with the physical mechanisms explained. The quasi-geostrophic equations, so well known in the Geophysical Fluid Dynamics (GFD) community, is derived with the Lorentz force present. The two-layer model is proposed as a simplified model for our studies. Progress with magnetically influenced barotropic and baroclinic instabilities are given, and some proposed future work concludes the document.

We present three dimensional hydrodynamic simulations of star-disc systems, focusing on the angular momentum evolution of the central object due to gravitational interactions with the disc. It is found that stellar spin-up is self-limited to approximately half its break-up speed. On long time-scales, we find that in simulations where m=1 is the dominant non-axisymetric mode, there is limited evolution in stellar spin. By contrast, in simulations where m=1 is non-dominant, we observe a monotonic decrease in stellar spin. Our experiments suggest a necessary condition for long-term spin down be that the system does not develop significant m=1 mode, which displaces the star from its center of mass.