Hydrodynamical interaction between a shock wave and a cloud . One dimensional approach

The collision of a plane parallel shock wave with a plane parallel cloud of uniform density is analysed for the case in which magnetic fields and radiative losses are not considered. General analytic solutions are discussed for the case in which the density of the cloud is greater than that of the surrounding environment. This problem generalises one of the classical problems in gas dynamics: the collision between a shock wave and a solid wall. The problem of the collision of a shock wave with a cloud has been intensely investigated in the past by several authors (see for example Klein et al. 1994 and references therein). The simplest assumption to make is to consider a cloud for which gravitational effects are not considered, magnetic fields are non-important and radiative losses are negligible. The fact that gravity is not taken into account, makes it possible to consider the density of the cloud as uniform. The complete 3D hydrodynamical problem is extremely complicated, even under the simplifications mentioned above. However, numerical simulations have been done for this case which ultimately give rise to instabilities causing a complete disruption of the cloud (Klein et al., 1994). This article describes how the solution of the one dimensional problem can be obtained. It has been argued in the past that at least for the case in which the density contrast is high, i.e. the ratio of the cloud's density to that of the external environment is high, the problem has to be very similar to the one found in the problem of a collision of a plane parallel shock with with a solid wall (Spitzer 1982, McKee 1988). Many Astrophysical phenomena give rise to collisions between a shock wave and a cloud. For example, when a supernova explosion occurs, the intense ejection of energy from the supernova into the interstellar medium produces a spherical shock wave which expands into the interstellar medium. Several examples exist for which collisions of this expanding shock have been observed to interact