Re$_{1}$) or inertia (high Re$_1$).

![Regime diagram of an initially round metal drop falling in a magma ocean, as a function of Re$_1$ and Bo. Markers correspond to numerical simulations. The dashed blue lines correspond to the relationship between Re$_1$ and Bo (eq. \[eq:Re=f(Bo)\]), for viscosities of the metal $\eta_1$ between $10^{-3}$ and $10^{-1}$ Pa.s. In the regime snapshots, the red lines correspond to the interface between metal and silicates and black vectors to the velocity field in a frame moving with the center of mass of the metal phase.[]{data-label="fig:drop_regime"}](drop_regime.pdf){width="0.9\linewidth"}

Though based on 2D simulations, our results are broadly consistent with published results from experiments and numerical simulations (in axisymmetric configurations) [*e.g.* @clift_1978; @han_1999; @landeau_2014].

At low Re$_1$, the drop remains undeformed, irrespectively of the value of Bo. The flow around the drop is laminar and stationary, and the drop develops an internal circulation. Keeping Bo small and increasing Re$_{1}$, the velocity field eventually becomes time-dependent, with the magnitude of the velocity fluctuations increasing with Re$_{1}$. The velocity fluctuations do deform the drop surface and modify its trajectory, leading to a *wobbling regime* [@clift_1978], but surface tension still remains large compared to the time-dependent inertial stresses, which prevents any significant 