It is a well-accepted hypothesis that deep-mantle primary plumes originate from a buoyant boundary layer at the Core-Mantle Boundary (CMB), where Rayleigh–Taylor (RT) instabilities play a key role in the plume initiation process. Combining 2D computational fluid dynamic (CFD) model simulations and a linear stability analysis, this article explores how a horizontal global flow in the mantle can influence the growth dynamics of RT instabilities in the source layer. Both the CFD simulation results and analytical solutions predict the global flows as a dampening factor to reduce their growth rates. It is found that layer-parallel global flow velocities (normalized to buoyancy driven upward flow velocity), U* > 30 completely suppress gravitational instabilities on short as well as long wavelengths, and force the entire system to advect in the horizontal direction. We present a series of real-scale numerical simulations to demonstrate the effects of Atwood number (