We study the evolution of structures in turbulent , self-gravitating media , and present an analytical criterion M _ { crit } \approx \epsilon _ { cascade } ^ { 2 / 3 } \eta ^ { -2 / 3 } G ^ { -1 } l ^ { 5 / 3 } ( where M _ { crit } is the critical mass , l is the scale , \epsilon _ { cascade } \approx \eta \sigma _ { v } ^ { 3 } / l is the turbulence energy dissipation rate of the ambient medium , G is the gravitational constant , \sigma _ { v } is the velocity dispersion , l is the scale and \eta \approx 0.2 is an efficiency parameter ) for an object to undergo quasi-isolated gravitational collapse .
The criterion also defines the critical scale ( l _ { crit } \approx \epsilon _ { cascade } ^ { 1 / 2 } \eta ^ { -1 / 2 } G ^ { -3 / 4 } \rho ^ { -3 / 4 } ) for turbulent gravitational instability to develop .
The analytical formalism explains the size dependence of the masses of the progenitors of star clusters ( M _ { cluster } \sim R _ { cluster } ^ { 1.67 } ) in our Galaxy .