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The convective Brinkman-Forchheimer equations given by  $$ \frac{\partial \boldsymbol{u}}{\partial t}-\mu\Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-1}\boldsymbol{u}+\nablap=\boldsymbol{f}, \ \nabla\cdot\boldsymbol{u}=0, $$ where $\mu,\alpha,\beta>0$and $r\in[1,\infty)$ describe the motion of incompressible fluid flows in asaturated porous medium. In bounded domains (for $d=2,3$ and $r\in[1,\infty)$),the existence of a weak martingale solution for stochastic convectiveBrinkman-Forchheimer equations forced by L\'evy noise consisting of a$\mathrm{Q}$-Wiener process and a compensated time homogeneous Poisson randommeasure is established in this work. Using the classical Faedo-Galerkinapproximation, a compactness method and a version of the Skorokhod embeddingtheorem for nonmetric spaces, we prove the existence of a weak martingalesolution. For $d=2$, $r\in[1,\infty)$ and $d=3$, $r\in[3,\infty)$, we provethat the martingale solution has stronger regularity properties such as itsatisfies the energy equality (It\^o's formula) and hence the trajectories areequal almost everywhere to an $\mathbb{H}$-valued c\`adl\`ag function definedon $[0, T ]$, ${\mathbb{P}}$-a.s. Furthermore, for $d=2$, $r\in[1,\infty)$ and$d=3$, $r\in[3,\infty)$ ($2\beta\mu\geq 1$ for $r=3$), we show the pathwiseuniqueness of solutions and use the classical Yamada-Watanabe argument toderive the existence of a strong solution and uniqueness in law.

Martingale solutions of two and three dimensional stochastic convective Brinkman-Forchheimer equations forced by L\'evy noise