Finite-size effects with rigid boundaries on nonequilibrium fluctuations in a liquid

In a recent publication [Physica A 291, 113 (2001)] the static structure factor of a liquid in a thermal nonequilibrium state was calculated exactly from the random Boussinesq equations, in the absence of convection, for “stress-free" boundary conditions. In the present paper we present a similar calculation, but with the more realistic “no-slip" boundary conditions. In this case an explicit calculation cannot be performed and we use a zeroth-order Galerkin approximation. The main conclusion is that the approximate structure factor thus calculated has qualitative the same behavior as the exact result for “stress-free" boundary conditions. The typical divergence on q-4 of the nonequilibrium part of the structure factor crosses over to a q2 dependence for extremely small wavevectors q. Separating both behaviors a maximum appears indicating that fluctuations with a particular wavevector, qmax, are maximally enhanced.