The Gravitational Instability of an Infinite Homogeneous Turbulent Medium

Jeans's analysis of the problem of the gravitational stability of an infinite homogeneous medium is examined and the need for including turbulence in the discussion is pointed out. The subject is then reconsidered from the point of view of the modern theories of turbulence, and it is shown how eddies in the density fluctuations which have wave numbers k < surd [4π G{ρ}/(c²+1/3{u²})] (where c denotes the velocity of sound and {u²} the mean square velocity of turbulence) are unstable in the sense that these fluctuations will grow with time.