3. The physical problem
We study the evolution of a cylindrical fluid jet impinging upon a cold heavy steady inhomogeneity, namely the cloud, in pressure equilibrium with the external medium. The relevant equations governing the jet evolution, for mass, momentum conservation, and radiative losses, are
where the fluid variables p, , and E are, as customary, pressure, density, velocity, and thermal energy () respectively; is the ratio of the specific heats; represents the radiative energy loss term (energy per unit volume per unit time, Raymond & Smith 1977).
The jet occupies initially a cylinder of length L. The initial flow structure has the following form:
where m is a `steepness' parameter for the shear layer separating the jet from the external medium (see Fig. 1). The choice of separating the jet's interior from the ambient medium with a smooth transition, instead of a sharp discontinuity, avoids numerical instabilities that can develop at the interface between the jet and the exteriors, especially at high Mach numbers.
Regarding the cloud, we fix its initial density and impose pressure equilibrium with respect to external medium; for simplicity we consider a steady cloud, with a thickness equal to the jet diameter.
© European Southern Observatory (ESO) 2000
Online publication: March 28, 2000