  We investigate the asymptotic limit of solutions to the Navier-Stokes-Fourier
system with the Mach number proportional to a small parameter $\varepsilon \to
0$, the Froude number proportional to $\sqrt{\varepsilon}$ and when the fluid
occupies large domain with spatial obstacle of rough surface varying when
$\varepsilon \to 0$. The limit velocity field is solenoidal and satisfies the
incompressible Oberbeck-Boussinesq approximation. Our studies are based on weak
solutions approach and in order to pass to the limit in a convective term we
apply the spectral analysis of the associated wave propagator (Neumann
Laplacian) governing the motion of acoustic waves.
