The turbulent destruction of clouds - I. A k-ǫ treatment of turbulence in 2D models of adiabatic shock-cloud interactions

The interaction of a shock with a cloud has been extensively studied in the literature, where the effects of magnetic fields, radiative cooling and thermal conduction have been considered. In many cases, the formation of fully developed turbulence has been prevented by the artificial viscosity inherent in hydrodynamical simulations. This problem is particularly severe in some recent simulations designed to investigate the interaction of a flow with multiple clouds, where the resolution of individual clouds is necessarily poor. Furthermore, the shocked flow interacting with the cloud has been assumed to be completely uniform in all previous single-cloud studies. In reality, the flow behind the shock is also likely to be turbulent, with non-uniform density, pressure and velocity structure created as the shock sweeps over inhomogenities upstream of the cloud (as seen in recent multiple cloud simulations). To address these twin issues we use a sub-grid compressible k-ǫ turbulence model to estimate the properties of the turbulence generated in shock-cloud interactions and the resulting increase in the transport coefficients that the turbulence brings. A detailed comparison with the output from an inviscid hydrodynamical code puts these new results into context. Despite the above concerns, we find that cloud destruction in inviscid and k-ǫ models occurs at roughly the same speed when the post-shock flow is smooth and when the density contrast between the cloud and inter-cloud medium, χ ∼ < 100. However, there are increasing and significant differences as χ increases. The k-ǫ models also demonstrate better convergence in resolution tests than inviscid models, a feature which is particularly useful for multiple-cloud simulations. Clouds which are over-run by a highly turbulent post-shock environment are destroyed significantly quicker as they are subject to strong “buffeting” by the flow. The decreased lifetime and faster acceleration of the cloud material to the speed of the ambient flow leads to a reduction in the total amount of circulation (vorticity) generated in the interaction, so that the amount of vorticity may be self-limiting. Additional calculations with an inviscid code where the post-shock flow is given random, grid-scale, motions confirms the more rapid destruction of the cloud. Our results clearly show that turbulence plays an important role in shock-cloud interactions, and that environmental turbulence adds a new dimension to the parameter space which has hitherto been studied.