Understanding the statistical properties of supersonic turbulence in hydrodynamical simulations

Abstract

Turbulence is a dominant feature operating in gaseous flows in a variety of systems, from aerodynamics to highly compressible media common in astrophysical environments. We present a systematic analysis of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We study a series of high-resolution, hydrodynamical grid simulations and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing as well as varying root mean square Mach numbers on the parameters describing the statistical state of the system. The probability density functions of the gas density, velocity, and the velocity increments are measured. Structure functions and power spectra are investigated to quantify the two-point correlation properties of compressible turbulence. We find that the mode of the forcing mechanism has an influence on the all measurements mentioned above. Compressively driven simulations show a more intermittent behaviour, a larger fractal dimension of the most dissipative structures (Chapter 4), a significantly larger density contrast with more pronounced wings of the density PDF (Chapter 5), and steeper power spectra with a decreased influence of the bottleneck effect (Chapter 6), at the same root mean square Mach number.