We present the first vertically resolved hydrodynamic simulations of a laterally propagating, deflagrating flame in the thin helium ocean of a rotating accreting neutron star. We use a new hydrodynamics solver tailored to deal with the large discrepancy in horizontal and vertical length scales typical of neutron star oceans, and which filters out sound waves that would otherwise limit our timesteps. We find that the flame moves horizontally with velocities of order $10^5$ cm s$^{-1}$, crossing the ocean in few seconds, broadly consistent with the rise times of Type I X-ray bursts. We address the open question of what drives flame propagation, and find that heat is transported from burning to unburnt fuel by a combination of top-to-bottom conduction and mixing driven by a baroclinic instability. The speed of the flame propagation is therefore a sensitive function of the ocean conductivity and spin: we explore this dependence for an astrophysically relevant range of parameters and find that in general flame propagation is faster for slower rotation and higher conductivity.
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