  This work deals with the asymptotic behavior of the two as well as three
dimensional convective Brinkman-Forchheimer (CBF) equations in periodic
domains: $$\frac{\partial\boldsymbol{u}}{\partial t}-\mu
\Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-1}\boldsymbol{u}+\nabla
p=\boldsymbol{f},\ \nabla\cdot\boldsymbol{u}=0,$$ where $r\geq1$. We prove that
the global attractor of the above system is a singleton under small forcing
intensity ($r\geq 1$ for $n=2$ and $r\geq 3$ for $n=3$ with $2\beta\mu\geq 1$
for $r=n=3$). After perturbing the above system with additive or multiplicative
white noise, the random attractor does not have a singleton structure. But we
obtain that the random attractor for 2D stochastic CBF equations with additive
and multiplicative white noise converges towards the deterministic singleton
attractor for $1\leq r\leq 2$ and $1\leq r<\infty$, respectively, when the
coefficient of random perturbation converges to zero (upper and lower
semicontinuity). Interestingly in the case of 3D stochastic CBF equations
perturbed by multiplicative white noise, we are able to establish that the
random attractor converges towards the deterministic singleton attractor for
$3\leq r\leq 5$ ($2\beta\mu\geq 1$ for $r=3$), when the coefficient of random
perturbation converges to zero.
