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