Non-autonomous 3D Brinkman-Forchheimer equation with singularly oscillating external force and its uniform attractor

For $\rho\in [0, 1)$ and $\varepsilon \gt 0$, the non-autonomous 3D Brinkman-Forchheimer equation with singularly oscillating external force $ \begin{align*} &u_t-\nu\Delta u+au+b|u|u+c|u|^\beta u+\nabla p = f_0(x,t)+\varepsilon^{-\rho}f_1(x,\frac{t}{\varepsilon}),\\ &\mathrm{div}u = 0 \end{align*} $ are considered, together with the averaged equation $ \begin{align*} &u_t-\nu\Delta u+au+b|u|u+c|u|^\beta u+\nabla p = f_0(x,t),\\ &\mathrm{div}u = 0 \end{align*} $ formally corresponding to the limiting case $\varepsilon = 0$. First, within the restriction $\rho \lt 1$ and under suitable translation-compactness assumptions on the external forces, the uniform (w.r.t.$\varepsilon$) boundedness of the related uniform attractors $\mathcal{A}^\varepsilon$ is established when $1 \lt \beta\leq 4/3$. This fact is not at all intuitive, since in principle the blow up of the oscillation amplitude might overcome the averaging effect due to the term $\frac{t}{\varepsilon}$ in $f_1$. Next, the convergence of the attractor $\mathcal{A}^\varepsilon$ of the first equation to the attractor $\mathcal{A}^0$ of the second one as $\varepsilon\rightarrow 0^+$ is established.