Characterizing the Velocity Fields in Massive Stars
  We apply the mathematical formalism of vector spherical harmonics decomposition to convective stellar velocity fields from multi-dimensional hydrodynamics simulations, and show that the resulting power spectra furnish a robust and stable statistical description of stellar convective turbulence. Analysis of the power spectra help identify key physical parameters of the convective process such as the dominant scale of the turbulent motions that influence the structure of massive evolved pre-supernova stars. We introduce the numerical method that can be used to calculate vector spherical harmonics power spectra from 2D and 3D convective shell simulation data. Using this method we study the properties of oxygen shell burning and convection for a 15 Msun star simulated by the hydrodynamics code FLASH in 2D and 3D. We discuss the importance of realistic initial conditions to achieving successful core-collapse supernova explosions in multi-dimensional simulations. We show that the calculated power spectra can be used to generate realizations of the velocity fields of pre-supernova convective shells. We find that the slope of the solenoidal mode power spectrum remains mostly constant throughout the evolution of convection in the oxygen shell in both 2D and 3D simulations. We also find that the characteristic radial scales of the convective elements are smaller in 3D than in 2D while the angular scales are larger in 3D. 
Emmanouil Chatzopoulos, Carlo Graziani, Sean M. Couch
astro-ph.SR