  The convective Brinkman-Forchheimer (CBF) equations characterize the motion
of incompressible fluid flows in a saturated porous medium. The small noise
asymptotic for the two-time-scale stochastic convective Brinkman-Forchheimer
(SCBF) equations in two and three dimensional bounded domains is carried out in
this work. More precisely, we establish a Wentzell-Freidlin type large
deviation principle for stochastic partial differential equations with slow and
fast time-scales, where the slow component is the SCBF equations in two and
three dimensions perturbed by small multiplicative Gaussian noise and the fast
component is a stochastic reaction-diffusion equation with damping. The results
are obtained by using a variational method (based on weak convergence approach)
developed by Budhiraja and Dupuis, Khasminkii's time discretization approach
and stopping time arguments. In particular, the results obtained from this work
are true for two dimensional stochastic Navier-Stokes equations also.
