While this model is a good first order-approximation, the devil is in the details and these details of cloud-shock interactions must be simulated by numerical means. This is a computationally taxing project and so understanding in the field comes with increases in computing power and algorithmic sophistication.
Some of the first model calculations were done by Sgro in 1975. He used a two dimensional square cloud. He showed that there was a critical density above which the cloud cooled quickly after being shocked and below which cooling was inefficient. Furthermore, he speculated that the external shock diffracts around the cloud and reconnects with itself. In this reconnection region, pressures are higher and the shock travels more quickly. Thus any dimple left by diffraction around a cloud will be evened out by the time the shock travels a few cloud diameters and will have no lasting effect on the shock front morphology.
Later models such as those performed by Bedogni & Woodward (1990) were expanded to cover a wider array of shock velocities and cloud-ISM density contrasts. Furthermore they assumed spherical clouds, cylindrical symmetry and a more sophisticated numerical hydrodynamic code. These models showed much the same results but a wealth of new details as well.
Again, when the external shock first encounters cloud a transmitted and reflected shock are set up (Figure 4a). The reflected shock becomes a bow shock if M>2.76 (Spitzer, 1982). While the cloud shock propagates, the external shock wraps around the cloud setting up secondary shocks driven obliquely into the cloud along the surface. When the blast wave reaches the downstream side of the cloud, it reconnects producing a region of transient high pressure and sending a second reflected shock back into into cloud (Figure 4b). A vortex system appears, the blast wave disconnects from the cloud and propagates onward.
The two cloud shocks move toward the center causing axial collapse (Figure 4b,c,d). Meanwhile the streaming post shock gas at sides of cloud form low density, low pressure zones by the Bernoulli principle and excite Kelvin-Helmholtz instabilities. Thus while the cloud is being crushed axially, it is expanding radially. When the two cloud shocks meet and pass each other, they begin to re-expand the cloud. Rayleigh-Taylor instabilities form clumps and K-H instabilities form vortices. Finally, the cloud is completely disrupted and fragmented (Figure 4e,f)
Bedogni & Woodward's models show the different morphologies that can be achieved by varying the Mach number and density contrast of the simulations. For high density clouds seem to survive more intact than low density clouds. Low shock velocities tend to leave a cloud roughly spherical as well whereas high velocities tend to produce streamers and vortex rings trailing downstream from the cloud.
Three dimensional calculations were carried out by, among others, Stone & Norman (1992) on spherical clouds. Figure 5 shows three frames from their simulation plotted with greyscale proportional to log density. In the left image, we see the spherical cloud beginning to collapse as the external shock (incident from the top) sweeps past. In the middle frame, the blast wave has detached, the reverse cloud shock has been initiated and turbulence has started on the downstream edge of the cloud. Notice some material has been pulled along with the blast wave. In the right-hand image fragmentation is well advanced and quite a lot of filamentary, turbulent structure is seen. Notice that the cloud as a whole is accelerated in the direction of the shock.
Stone and Norman manage to reproduce nearly all the details seen in earlier two-dimensional work and found that, what are seen as 'vortex rings' in the 2-D simulations, are unstable in three dimensions. Instead vortex filaments are formed. Significant turbulent mixing and filamentary structure was produced just as in the 2-D models. Furthermore, they found that the degree of fragmentation and the size of the fragments seen was directly correlated with their simulation resolution.