Simplified hydrodynamic theory of nonlocal stationary state fluctuations

In the realsitic approximation that the expansion coefficient of a fluid vanishes, the hydrodynamic fluctuations around a steady state characterized by a small temperature gradient are determined entirely by the variations of the strength of the random forces from point to point. The assumption of local hydrodynamic equilibrium for the random forces leads to a long-range static density momentum correlation, as well as to a significant odd-in-frequency correction to the Brillouin light scattering, whose integrated intensity agrees with other work of Ronis et al. and Kirkpatrik et al. Consequences of the long-range correlations for $\frac{1}{f}$ noise ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and local equilibrium postulates are discussed.