Non-linear convection due to compositional and thermal buoyancy in Earth's outer core

► Derivation of Landau-Ginzburg type equations near the onset stationary and oscillatory convection. ► Nusselt number contribution and occurrence of Eckhaus and zigzag instability at the onset of staionary convection. ► The stability regions of standing and traveling waves. ► Occurrence of Bejamin-Feir instability at the onset of oscillatory convection.