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

**Doris Folini (1), Rolf Walder (2,3)**

1 - Institute of Astronomy, ETH Zurich, Switzerland

2 - Observatoire de Strasbourg, 67000 Strasbourg, France

3 - Max-Planck-Institut fur Astrophysik, 85741 Garching, Germany

Colliding hypersonic flows play a decisive role in many

astrophysical objects. They contribute, for example, to molecular

cloud structure, the X-ray emission of O-stars, differentiation of

galactic sheets, the appearance of wind-driven structures, or,

possibly, the prompt emission of $\gamma$-ray bursts. Our intention

is the thorough investigation of the turbulent interaction zone of

such flows, the cold dense layer (CDL). In this paper, we

focus on the idealized model of a 2D plane parallel isothermal slab

and on symmetric settings, where both flows have equal parameters.

We performed a set of high-resolution simulations with upwind Mach

numbers, $5 < M_{\mathrm{u}} < 90$.

We find that the CDL is irregularly shaped and has a patchy and

filamentary interior. The size of these structures increases with

$\ell_{\mathrm{cdl}}$, the extension of the CDL. On average, but not

at each moment, the solution is about self-similar and depends only

on $M_{\mathrm{u}}$. We give the corresponding analytical

expressions, with numerical constants derived from the simulation

results. In particular, we find the root mean square Mach number to

scale as $M_{\mathrm{rms}} \approx 0.2 M_{\mathrm{u}}$. Independent

of $M_{\mathrm{u}}$ is the mean density, $\rho_{\mathrm{m}} \approx

30 \rho_{\mathrm{u}}$. The fraction $f_{\mathrm{eff}}$ of the upwind

kinetic energy that survives shock passage scales as

$f_{\mathrm{eff}}= 1 - M_{\mathrm{rms}}^{-0.6}$. 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.

**Reference: **Astronomy and Astrophysics

Status: Manuscript has been accepted

**Weblink: **http://fr.arxiv.org/abs/astro-ph/0606753

**Comments: **

**Email: **folini@astro.phys.ethz.ch