Three-Dimensional Parallel Lattice Boltzmann Hydrodynamic Simulations of Turbulent Flows in Interstellar Dark Clouds

Ph.D. thesis by Dirk Muders, MPIfR


Exploring the clumpy and filamentary structure of interstellar molecular clouds is one of the key problems of modern astrophysics. So far, we have little knowledge of the physical processes that cause the structure, but turbulence is suspected to be essential. In this thesis I study turbulent flows and how they contribute to the structure of interstellar dark clouds. To this end, three-dimensional numerical hydrodynamic simulations are needed since the detailed turbulent spatial and velocity structure cannot be analytically calculated. I employ the "Lattice Boltzmann Method", a recently developed numerical method which solves the Boltzmann equation in a discretized phase space. Mesoscopic particle packets move with fixed velocities on a Cartesian lattice and at each time step they exchange mass according to given rules. Because of its mainly local operations the method is well suited for application on parallel or clustered computers.

As part of my thesis I have developed a parallelized hydrodynamics code. I have improved the numerical stability for Reynolds numbers up to ~30000 and Mach numbers up to 0.9 and I have extended the method to include a second miscible fluid phase. The code has been used on the three currently most powerful workstations at the "Max-Planck-Institut für Radioastronomie" in Bonn and on the massively parallel mainframe Connection Machine 5 (CM-5) at the "Gesellschaft für Mathematik und Datenverarbeitung" in St. Augustin. The simulations consist of collimated shear flows and the motion of molecular clumps through an ambient medium. The dependence of the emerging structure on Reynolds and Mach numbers is studied.

The main results are (1) that distinct clumps and filaments appear only at the transition between laminar and fully turbulent flow at Reynolds numbers between 500 and 5000 and (2) that subsonic viscous shear flows are capable of producing the dark cloud velocity structure. The unexpectedly low Reynolds numbers can be explained by the enlargement of the gas viscosity by magnetic fields of the order 10 micro-Gauss and the strong coupling between ionized and neutral gas. The occurrance of well-defined structure between the highly ordered laminar and the chaotic turbulent flow regimes can be interpreted in the framework of the "Edge of Chaos", i.e. the tendency of complex systems to exist only at the transition between phases. In order to compare the simulations with observed data I have used the 100m radio telescope at Effelsberg to map the ground transition of sulphur monoxide toward the quiescent cold dark cloud L1512. The data show a clumpy structure that I interpret as a turbulent tail behind the dense central cloud.

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