Supersonic turbulence in 3D isothermal flow collision

¹ École Normale Supérieure, Lyon, CRAL, UMR CNRS 5574, Université de Lyon, 69364 Lyon Cedex 7, France
e-mail: doris.folini@ens-lyon.fr
² Swiss National Supercomputing Center, CSCS Lugano, 6900 Lugano, Switzerland

Received: 11 August 2012
Accepted: 17 December 2013

Abstract

Large scale supersonic bulk flows are present in a wide range of astrophysical objects, from O-star winds to molecular clouds, galactic sheets, accretion, or γ-ray bursts. Associated flow collisions shape observable properties and internal physics alike. Our goal is to shed light on the interplay between large scale aspects of such collision zones and the characteristics of the compressible turbulence they harbor. Our model setup is as simple as can be: 3D hydrodynamical simulations of two head-on colliding, isothermal, and homogeneous flows with identical upstream (subscript u) flow parameters and Mach numbers 2 < M_u < 43. The turbulence in the collision zone is driven by the upstream flows, whose kinetic energy is partly dissipated and spatially modulated by the shocks confining the zone. Numerical results are in line with expectations from self-similarity arguments. The spatial scale of modulation grows with the collision zone. The fraction of energy dissipated at the confining shocks decreases with increasing M_u. The mean density is ρ_m ≈ 20ρ_u, independent of M_u. The root mean square Mach number is M_rms ≈ 0.25M_u. Deviations toward weaker turbulence are found as the collision zone thickens and for small M_u. The density probability function is not log-normal. The turbulence is inhomogeneous, weaker in the center of the zone than close to the confining shocks. It is also anisotropic: transverse to the upstream flows M_rms is always subsonic. We argue that uniform, head-on colliding flows generally disfavor turbulence that is at the same time isothermal, supersonic, and isotropic. The anisotropy carries over to other quantities like the density variance – Mach number relation. Line-of-sight effects thus exist. Structure functions differ depending on whether they are computed along a line-of-sight perpendicular or parallel to the upstream flow. Turbulence characteristics generally deviate markedly from those found for uniformly driven, supersonic, isothermal turbulence in 3D periodic box simulations. We suggest that this should be kept in mind when interpreting turbulence characteristics derived from observations. Our simulations show that even a simple model setup results in a richly structured interaction zone. The robustness of our findings toward more realistic setups remains to be tested.