Astron. Astrophys. 324, L21-L24 (1997)

5. Conclusion

The initial conjecture that spectral transfer is reduced for waves with length smaller but comparable to the Jeans length is validated by our numerical experiments, which agree reasonably well with the phenomenological relation (2) between Mach number and wave number (or Jeans number). Such an inhibition of nonlinear interactions in fluids by dispersive effects is not unique; geostrophic turbulence also presents at large scales a similar phenomenon (Rhines 1979, Dubrulle and Valdettaro 1992). Non-dispersive (MHD) Alfvén waves in conducting fluids also provide an interesting case of decrease of nonlinear coupling, due to the specificity of the nonlinear coupling, actually leading to dispersive-like effects (Iroshnikov 1963, Kraichnan 1965, Grappin and Mangeney 1996).

For the present mechanism to play a role in sustaining the fully developed turbulence of interstellar matter, it is however necessary that dispersion effects be important in a spectral domain larger than considered above. For this to actually happen, it is sufficient to assume that the pressure gradient roughly balances the gravitational forces not only at a definite scale, but in the whole spectral range where the condensations are observed, since this is a sufficient condition for dispersive effects to be important. This assumption is compatible with observations, which indicate that the Jeans number is close to unity for a whole range of scales. This scenario does no longer require to invoke the so-called "turbulent pressure", which effect has been demonstrated only in artificially forced cases, (Léorat et al., 1990). To test this hypothesis numerically requires considering a hierarchy of condensations all close to pressure equilibrium, a situation very different from the uniform case considered here (work in progress).

We thank ASCI (Applications Scientifiques du Calcul Intensif) for hospitality during part of this work and IDRIS for providing numerical facilities.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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