Turbulence has been believed to play a key role in the dynamics of molecular clouds for a long time (see for example Larson 1981; Myers 1983; Scalo 1987; Scalo 1990; Falgarone & Phillips 1990; Falgarone et al. 1994; Ballesteros-P. et al. 1999; Pety & Falgarone 2000). However, many questions are still subject to debate. What is the origin of that turbulence? Is compressibility an essential feature? What is the role of the magnetic field (e.g. Myers & Khersonsky 1995)? How does the velocity field couple to other aspects of interstellar cloud dynamics? The origin of these difficulties can be traced to at least two facts:
Progress has been made recently along two lines. Lis et al. (1996), Lis et al. (1998), Miesch & Scalo (1995) and
Miesch et al. (1999) have analysed the Probability Distribution Functions (PDF)
of line centroid velocity increments (see Appendix B).
These quantities are the closest available to velocity increment PDFs
widely used in laboratory experiments on turbulence (see Frisch 1995,
for the necessary background). These PDFs suggest that intermittency
is present in the turbulent velocity field. However, their best maps
come from the 
Ophiuchi cloud which exhibits an active
star formation region, and it is not clear whether the velocity field
is characteristic of turbulence alone or dominated by the interactions
between newly-formed YSOs and the embedding gas. Statistical analyses
have also been carried out, for example by Padoan et al. (1999).
Although starting with very different assumptions, Stutzki et al. (1998) and Mac Low & Ossenkopf (2000) developed an analysis based on a form of wavelet transform (either directly or via some related mathematical tools). They have shown that quantitative information can be extracted in that way, but their results are plagued by a low signal-to-noise ratio and a lack of scale dynamics, which leads to heavy uncertainties. Furthermore, it is far from obvious how to use these results in order to gain a deeper understanding of the underlying physics.
Whatever the detailed characteristics of the velocity field inside
a molecular cloud, its influence on the dynamics of the gas and thus
on the interpretation of observational quantities has to be taken
into account. The first and most obvious effect is the interpretation
of line width as Doppler broadening. This gives a simple measure of
a typical velocity dispersion within the emitting region. In quiescent
clouds, that value is usually much higher than the pure thermal broadening
and controls the radiative cooling of the gas. There is now a fairly
well-established relation between velocity dispersion and the size
of the emitting region (
,
with
(see e.g. Miesch & Bally 1994)). Evidence of high clumpiness
of the cloud density, or even of fractal structure may be found e.g.
in Falgarone et al. (1991) or Falgarone et al. (1994) and references therein.
An elaborate analysis of the interaction between line formation and a turbulent velocity field is given by Kegel et al. (1993) and Piehler & Kegel (1995) who compute the effects of a finite correlation length within a cloud (see also Park & Hong 1995). These computations prove that line profiles may be significantly modified and that neither micro- nor macro-turbulence approximations are usually valid. However, their cloud models are far too simple to take into account the real structure of a cloud and their mean field approach neglects realisation effects in any specific object. The latter point has been stressed by Rousseau et al. (1998), but their model is otherwise too qualitative and remote from observational aspects to shed much light on the physics of "real'' clouds.
Another potentially important influence of turbulence is on the chemical
evolution of molecular clouds. A number of key chemical species have
observational abundances far larger than what any model predicts.
The best case is that of
whose only formation
route requires an energy of 4640 K, and is widely observed.
Intermittent dissipation of turbulence has been proposed as the source
of heat that could drive the formation. Since that dissipation occurs
in a small fraction of volume (typically less than 10-3),
the overall gas temperature is not affected. Joulain et al. (1998) have proposed
a model of chemistry within one specific vortex that supports well
that mechanism. Following Falgarone & Puget (1995), turbulence may also induce a
decoupling between gas and grains that leads to a high relative velocity
of the two fluids. The kinetic energy released in a gas-grain collision
then exceeds the thermal one and could help to drive slightly endothermic
reactions or increase collisional excitation.
It can be seen that the induced effects of a turbulent velocity field do not rely upon the fact that interstellar turbulence complies with what is implied by a canonical academic description of turbulence in fluids. Most phenomena follow only from the existence of a large deviation to from a Gaussian distribution of some properties of the velocity field (not necessarily the velocity components themselves). Therefore, in an attempt to study those effects, we do not need to solve the Navier-Stokes equations at a high Reynolds number in a compressible gas in order to build a realistic velocity field. Such a task is out of reach of present computing facilities, and even if achieved would leave no computing power to deal with chemistry, radiative transfer, and other intensive computing tasks. What we need is a velocity field compatible with all (or most) observational constraints. Then, once that field is built and characterised, it can be used as an input for a model of molecular clouds, and the effects of varying the velocity field measured in the model.
In this paper, we have tried to follow such a program (or at least the first steps of it). Current work on incompressible turbulence in the laboratory leads us to believe that the intrinsically multi-scale character of turbulence can only be grasped with a specifically multi-scale tool, namely wavelet transform.
In Sect. 2, we gather observational data and submit them to an analysis that extracts a small number of parameters that quantify interstellar turbulence under the assumption that results on incompressible terrestrial turbulence can be extended to compressible interstellar turbulence. In Sect. 3, we use these parameters to build a synthetic velocity field whose statistical properties are identical to the observed ones. In Sect. 4 we build a 1D time-dependent lattice dynamical network that is the frame on which our interstellar cloud model is built. In Sect. 5 we present a toy model chemistry with some qualitative properties of interstellar chemistry. In Sect. 6 that chemistry is coupled to the velocity field, and the structures that follow are illustrated. Section 7 is our conclusion.
Copyright ESO 2002