  We look for a simple analytic model to distinguish between stellar clusters
undergoing a bimodal hydrodynamic solution from those able to drive only a
stationary wind. Clusters in the bimodal regime undergo strong radiative
cooling within their densest inner regions, which results in the accumulation
of the matter injected by supernovae and stellar winds and eventually in the
formation of further stellar generations, while their outer regions sustain a
stationary wind. The analytic formulae are derived from the basic hydrodynamic
equations. Our main assumption, that the density at the star cluster surface
scales almost linearly with that at the stagnation radius, is based on results
from semi-analytic and full numerical calculations. The analytic formulation
allows for the determination of the threshold mechanical luminosity that
separates clusters evolving in either of the two solutions. It is possible to
fix the stagnation radius by simple analytic expressions and thus to determine
the fractions of the deposited matter that clusters evolving in the bimodal
regime blow out as a wind or recycle into further stellar generations.
