The turbulent destruction of clouds - I. Ak-ε treatment of turbulence in 2D models of adiabatic shock-cloud interactions

Abstract

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 inhomogeneities upstream of the cloud (as seen in recent multiple cloud simulations). To address these twin issues we use a subgrid compressible k–ε 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–ε models occurs at roughly the same speed when the post‐shock flow is smooth and when the density contrast between the cloud and intercloud medium, χ≲ 100. However, there are increasing and significant differences as χ increases. The k–ε 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 confirm 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.

The interaction of a magnetohydrodynamical shock with a filament

“…5 presents snapshots of the time evolution of the density distribution for simulation m10c1b1l4o45pa. The evolution of the filament broadly follows the stages outlined in section 4.1 of Pittard et al (2009). First, the filament is struck and compressed by the shock front, and a bow shock is formed.…”

“…We are therefore able to vary the aspect ratio and orientation of the filament in order to investigate how such a change might alter the interaction. The filament has been given smooth edges over about 10 per cent of its radius, using the density profile from Pittard et al (2009), with p 1 = 10 giving a reasonably sharp-edged cloud. The filament and surrounding ambient medium are in pressure equilibrium.…”

“…Pittard & Goldsmith (2016) compared all three time-scales and found that the one defined by Xu & Stone (1995) for prolate clouds gave a slightly better reduction in variance between the simulations. Therefore, this time-scale, t cs , has been adopted for this paper, with the assumption that the smooth edges to the filament can be approximated as reasonably sharp edges (Pittard et al 2009). Several other time-scales are available.…”

Observability and diagnostics in the X-ray band of shock-cloud interactions in supernova remnants

“…As in the case of magnetized clouds (Orlando et al 2008), shocked clouds with considerable particle acceleration would fall in-between the limit of completely suppressed thermal conduction (HY runs) and the unmagnetized limit of conduction (RC runs) discussed in this paper. Pittard et al (2009) demonstrated that turbulence plays an important role in shock-cloud interactions, and that environmental turbulence adds a new dimension to the parameter space. In particular, these authors showed that turbulence is generated mainly around the cloud boundary and in the cloud wake after ∼τ cc , the main effect being that clouds subject to a highly turbulent post-shock environment are destroyed significantly more rapidly than those within a smooth flow: the greater the cloud density contrast χ, the higher the effect of turbulence (for instance, for χ ≈ 100, the effect of the post-shock turbulence dominates the shock-cloud interaction).…”

“…In particular, these authors showed that turbulence is generated mainly around the cloud boundary and in the cloud wake after ∼τ cc , the main effect being that clouds subject to a highly turbulent post-shock environment are destroyed significantly more rapidly than those within a smooth flow: the greater the cloud density contrast χ, the higher the effect of turbulence (for instance, for χ ≈ 100, the effect of the post-shock turbulence dominates the shock-cloud interaction). On the other hand, an efficient thermal conduction smooths the cloud boundary very quickly (see Paper I), and turbulence grows more slowly around clouds with a smooth density profile (Pittard et al 2009). Thus we are confident that our results are valid and the diagnostics proposed here can be applied to clouds of moderate density contrast (i.e., the effects of turbulence poorly influence the shockcloud interaction at early evolutionary stages for t < τ cc ) and smooth density profiles (i.e., the growth of turbulence around clouds is slow), which we have considered here.…”