Adaptive Mesh Refinement for Supersonic Molecular Cloud Turbulence

We present the results of three-dimensional numerical simulations of supersonic isotropic Euler turbulence with adaptive mesh refinement (AMR) and effective grid resolution up to 10243 zones. Our experiments describe nonmagnetized, driven turbulent flows with an isothermal equation of state. Mesh refinement on shocks and shear is implemented to resolve dynamically important structures and calibrated to match the turbulence statistics obtained from the equivalent uniform-grid simulations. We demonstrate that as soon as the integral and dissipation scales are sufficiently separated, further increasing the resolution does not require mesh refinement all over the computational domain. The volume of finer subgrids in our AMR simulations scales with linear resolution approximately as N-1. Turbulence statistics derived from our AMR simulations and simulations performed on uniform grids agree surprisingly well, even though only a fraction of the volume is covered by AMR subgrids. We show that subdimensional nested "Mach cones" and U-shaped shocklets dominate the dynamics in supersonic turbulent flows. Based on these results, we discuss the fractal dimension of dissipative structures, their signature in the statistical properties of supersonic turbulence, and their role in overall flow dynamics.

[1]  She,et al.  Universal scaling laws in fully developed turbulence. , 1994, Physical review letters.

[2]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[3]  D. O. Astronomy,et al.  Interstellar Turbulence I: Observations and Processes , 2004, astro-ph/0404451.

[4]  Kai Germaschewski,et al.  ADAPTIVE MESH REFINEMENT FOR SINGULAR SOLUTIONS OF THE INCOMPRESSIBLE EULER EQUATIONS , 1998 .

[5]  Dinshaw S. Balsara,et al.  Higher order Godunov schemes for isothermal hydrodynamics , 1994 .

[6]  P. Padoan,et al.  The Stellar Initial Mass Function from Turbulent Fragmentation , 2000, astro-ph/0011465.

[7]  P. Colella,et al.  Local adaptive mesh refinement for shock hydrodynamics , 1989 .

[8]  Dubrulle,et al.  Intermittency in fully developed turbulence: Log-Poisson statistics and generalized scale covariance. , 1994, Physical review letters.

[9]  P. Woodward,et al.  Convergence Tests for the Piecewise Parabolic Method and Navier—Stokes Solutions for Homogeneous Compressible Turbulence , 2000 .

[10]  Uriel Frisch,et al.  A simple dynamical model of intermittent fully developed turbulence , 1978, Journal of Fluid Mechanics.

[11]  Bruce G. Elmegreen,et al.  A FRACTAL ORIGIN FOR THE MASS SPECTRUM OF INTERSTELLAR CLOUDS , 1996 .

[12]  C. Brunt.  Large-Scale Turbulence in Molecular Clouds , 2003 .

[13]  S. Boldyrev.  Kolmogorov-Burgers Model for Star-forming Turbulence , 2001, astro-ph/0108300.

[14]  E. Siggia,et al.  Collapsing solutions to the 3‐D Euler equations , 1990 .

[15]  T. Passot,et al.  Density probability distribution in one-dimensional polytropic gas dynamics , 1998, physics/9802019.