3.2. Ablation

The motion of clouds with respect to the ambient hot medium leads to Kelvin-Helrnholtz and Rayleigh-Taylor instabilities, which can break up the clouds into smaller pieces and accelerate mass exchange between the phases. Both instabilities operate on time scales t_i ~ (_c / _h)^1/2 r_c / v, where v is the relative speed between the cloud and the hot medium and _c / _h ~ T_h/T_c in pressure equilibrium. Most studies have concentrated on the fate of a cloud overtaken by a strong supernova or spiral density-wave shock (Woodward 1976; Nittman, Falle and Gaskell 1982; Heathcote and Brand 1983; McKee 1988; Klein, McKee and Colella 1989). in this case t_i is of the same order as the "cloud-crushing" time, t_cc, which is the time scale required for a secondary shock to be driven into a cloud once it is overrun by the main shock (McKee 1988). The cloud destruction process is accelerated by the significant pressure differential between the sides of the cloud and its front and back (Nittman, Falle and Gaskell 1982). The unbalanced forces cause the cloud to "pancake", i.e., to spread sideways, and the increase in cross-section speeds up the momentum deposition which tears apart the cloud. Pressure fluctuations and vorticity generation arising from the interactions of multiple shocks also play an important role in cloud disruption (Klein, McKee and Colella 1989).

The time scale for ablated cloud material to be effectively mixed with the intercloud medium should lie somewhere between t_i and the hydrodynamic drag time, t_d ~ (_c / _h) r_c/v. Nulsen (1982), using the longer time scale t_d, estimated that cold gas would be ablated from a cloud at a rate _ab ~ r²_{c h} v. If thermal conduction were negligible, the cloud would leave behind a cylindrical "trail" with a radius ~ r_c, containing cold material with a mean density <>_tr ~ _h. If the ablated gas is well-mixed with the hot phase downstream of the cloud, as we might expect from a turbulent ablation process, then the global time scale for cooling the hot phase by ablation is simply the time required for the trails to fill space, t_ab ~ r_c / fv, where f is the filling factor in clouds. t_ab is shorter than the cloud disruption time if the clouds contain more mass than the hot phase, and it is longer than the saturated evaporation time by a f actor ~ ^-1, where is the Mach number of cloud motion relative to the hot phase.

For diffuse interstellar clouds moving through the hot phase of the ISM in the Milky Way, ~ 0.1. According to the Nulsen (1982) model, ablation from subsonically moving clouds is a less important mechanism for destroying clouds than conduction in the saturated limit, but may be more important than conduction in the classical limit, i.e., for large clouds. For clouds moving nearly sonically, e.g., randomly moving clouds in the spheroidal component of a galaxy, hydrodynamical instabilities are probably the most efficient mechanism for shredding clouds to the point where thermal mixing via conduction is very efficient.

Lateral expansion of the cloud can shorten the hydrodynamic drag time considerably (Nittman, Falle and Gaskell 1982; Klein, McKee and Colella 1989). Klein, McKee and Colella find that the drag time is of order t_i for density contrasts _c / _h as high as 100, but for much larger density contrasts the cloud is torn apart before it slows significantly. These calculations suggest that mixing can occur much more rapidly than predicted by the Nulsen (1982) model. Further numerical simulations capable of following the mixing process with high resolution are clearly needed to test the basic assumptions of any ablation model.