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

In a recent publication [Physica A 291, 113 (2001)] the static structure fa ctor of a liquid in a thermal nonequilibrium state was calculated exactly f rom the random Boussinesq equations, in the absence of convection, for "str essfree" boundary conditions. In the present paper we present a similar cal culation, but with the more realistic "no-slip" boundary conditions. In thi s case an explicit calculation cannot be performed and we use a zeroth-orde r Galerkin approximation. The main conclusion is that the approximate struc ture 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 q(2 ) dependence for extremely small wavevectors q. Separating both behaviors a maximum appears indicating that fluctuations with a particular wavevector, q(max), are maximally enhanced.