Supersonic turbulence in shock-bound interaction zones I: symmetric settings

Colliding hypersonic flows play a decisive role in many astrophysical objects. In this paper, we look at the idealized model of a 2D plane parallel isothermal slab (CDL) and at symmetric settings, where both flows have equal parameters. We performed a set of high-resolution simulations with upwind Mach numbers, 5 < M_u < 90. We find that the CDL is irregularly shaped and has a patchy and filamentary interior. The size of these structures increases with l_cdl, the extension of the CDL. On average, but not at each moment, the solution is about self-similar and depends only on M_u. We find the root mean square Mach number to scale as M_rms ~ 0.2 M_u. Independent of M_u is the mean density, rho_m ~ 30 rho_u. The fraction f_eff of the upwind kinetic energy that survives shock passage scales as f_eff= 1 - M_rms^(-0.6). This dependence persists if the upwind flow parameters differ from one side to the other of the CDL, indicating that the turbulence within the CDL and its driving are mutually coupled. In the same direction points the finding that the auto-correlation length of the confining shocks and the characteristic length scale of the turbulence within the CDL are proportional. In summary, larger upstream Mach numbers lead to a faster expanding CDL with more strongly inclined confining interfaces relative to the upstream flows, more efficient driving, and finer interior structure relative to the extension of the CDL