Hydrodynamic time correlation functions in the presence of a gravitational field

This paper shows that the ordinary Brillouin spectrum peaks associated to scattered radiation of acoustic modes in a fluid suffer a shift in their values due to gravitational effect. The approach is based on the ordinary linearized Navier–Stokes equations for a fluid coupled to a Newtonian gravitational potential. The formalism leads to a dispersion relation that contains both gravitational and dissipative effects. It is also shown that the Brillouin peaks tend to condense into a single peak when the fluid modes approach the critical Jeans wave number.