Supersonic turbulence in shock-bound interaction zones

D. Folini; R. Walder

doi:doi:10.1051/0004-6361:20053898

Free access

Issue		A&A Volume 459, Number 1, November III 2006


Page(s)		1 - 19
Section		Astrophysical processes
DOI		http://dx.doi.org/10.1051/0004-6361:20053898

A&A 459, 1-19 (2006)
DOI: 10.1051/0004-6361:20053898

I. Symmetric settings

D. Folini¹ and R. Walder^{2, 3}

¹ Institut für Astronomie, ETH Zürich, 8092 Zürich, Switzerland
e-mail: folini@astro.phys.ethz.ch
² Observatoire de Strasbourg, 67000 Strasbourg, France
e-mail: walder@astro.phys.ethz.ch
³ Max-Planck-Institut für Astrophysik, 85741 Garching, Germany

(Received 24 July 2005 / Accepted 26 June 2006 )

Abstract
Colliding hypersonic flows play a decisive role in many astrophysical objects. They contribute, for example, to the molecular cloud structure, the X-ray emission of O-stars, differentiation of galactic sheets, appearance of wind-driven structures, or, possibly, to the prompt emission of $\gamma$ -ray bursts. Our intention is 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, $5 < M_{{\rm u}} < 90$ .

We find that the CDL is irregularly shaped and has a patchy and filamentary interior. The size of these structures increases with $\ell_{{\rm cdl}}$ , the extension of the CDL. On average, but not at each moment, the solution is nearly self-similar and only depends on $M_{{\rm u}}$ . 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 $M_{{\rm rms}} \approx 0.2~M_{{\rm u}}$ . The mean density, $\rho_{{\rm m}} \approx 30~\rho_{{\rm u}}$ is independent of $M_{{\rm u}}$ . The fraction $f_{{\rm eff}}$ of the upwind kinetic energy that survives shock passage scales as $f_{{\rm eff}}= 1 - M_{{\rm rms}}^{-0.6}$ . 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. Another finding points in the same direction, namely that the auto-correlation length of the confining shocks and the characteristic length scale of the turbulence within the CDL are proportional. Larger upstream Mach-numbers lead to a faster expanding CDL, confining interfaces that are less inclined with respect to the upstream flow direction, more efficient driving, and finer interior structure with respect to the extension of the CDL.

Key words: shock waves -- instabilities -- turbulence -- hydrodynamics -- ISM: kinematics and dynamics -- stars: winds, outflows

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