Modification of nonequilibrium fluctuations by interaction with surfaces

Fluctuating hydrodynamics is used to calculate the density correlation function and light-scattering spectrum for a fluid in a stationary temperature gradient. The non-plane-wave nature of the light source in the direction of the temperature gradient is considered explicitly. Finite-size effects are shown to be important when the ratio of system size to dynamic correlation length is smaller than or equal to $O\left(1\right)\mathrm{}$. The magnitude and size of the asymmetry of the Brillouin peaks, as well as the line shapes, are found to depend strongly on the scattering wave vector, beam width, and system size, while the dependence on the surface reflection coefficient is much weaker than expected. The importance of including surface fluctuations when absorbing walls are used is discussed.