On the hydrodynamic interaction of shock waves with interstellar clouds. II. The effect of smooth cloud boundaries on cloud destruction and cloud turbulence

The effect of smooth cloud boundaries on the interaction of steady planar shock waves with interstellar clouds is studied using a local adaptive mesh refinement technique with an axisymmetric Godunov hydrodynamic scheme. A three-dimensional calculation is also done to confirm the two-dimensional results. We find that smooth cloud boundaries significantly affect cloud morphology and retard cloud destruction. After shock passage, a sharp density jump forms due to velocity gradients generated in the smooth cloud boundary. We refer to this density jump as a slip surface because the velocity is sheared parallel to its surface. The formation of a slip surface leads to complete cloud destruction because of the Kelvin-Helmholtz and Rayleigh-Taylor instabilities. We construct analytic models of cloud drag and vorticity generation that compare well with the numerical results. Small shreds formed by the instabilities have significant velocity dispersions of 10%-20% of the ambient shock velocity. They could be related to the small cold H (I) clouds recently observed by Stanimirovic & Heiles. The dependence of the velocity dispersion on region size, the so-called line width-size relation, is found to be time-dependent. In the early stages, the line width-size relation is more or less flat because of the significant small-scale fluctuations generated by the Kelvin-Helmholtz instability. In the later stages, the small-scale fluctuations tend to damp, leading to a line width that increases with size. The possibility of gravitational instability triggered by shock compression is discussed. We show that gravitational collapse can be induced in an initially uniform cloud by a radiative shock (gamma < 4/3) only if it is not too strong and nonthermal motions are weak.