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The long time behavior of Wong-Zakai approximations of 2D as well as 3Dnon-autonomous stochastic convective Brinkman-Forchheimer (CBF) equations withnon-linear diffusion terms on bounded and unbounded ($\mathbb{R}^d$ for$d=2,3$) domains is discussed in this work. To establish the existence ofrandom pullback attractors, the concept of asymptotic compactness (AC) is used.In bounded domains, AC is proved via compact Sobolev embeddings. In unboundeddomains, due to the lack of compact embeddings, the ideas of energy equationsand uniform tail estimates are exploited to prove AC. In the literature, CBFequations are also known as \emph{Navier-Stokes equations (NSE) with damping},and it is interesting to see that the modification in NSE by linear andnonlinear damping provides better results than that available for NSE. Thepresence of linear damping term helps to establish the results in the wholedomain $\mathbb{R}^d$. The nonlinear damping term supports to obtain betterresults in 3D and also for a large class of nonlinear diffusion terms.Moreover, we prove the existence of a unique random pullback attractor forstochastic CBF equations with additive white noise. Finally, for additive aswell as multiplicative noise case, we establish the convergence of solutionsand upper semicontinuity of random pullback attractors for Wong-Zakaiapproximations of stochastic CBF equations towards the random pullbackattractors for stochastic CBF equations when correlation time of colored noiseconverges to zero.

Long term behavior of 2D and 3D non-autonomous random convective Brinkman-Forchheimer equations driven by colored noise