We investigate numerically the surface flow on the secondary star during outbursts. We use a simple model for the irradiation and the geometry of the secondary star: the irradiation temperature is treated as a free parameter and the secondary is repl
aced by a spherical star with a space-dependent Coriolis force that mimics the effect of the Roche geometry. The Euler equations are solved in spherical coordinates with the TVD-MacCormack scheme. We show that the Coriolis force leads to the formation of a circulation flow from high latitude region to the close vicinity of the $L_1$ point. However no heat can be efficiently transported to the $L_1$ region due to the rapid radiative cooling of the hot material as it enters the equatorial belt shadowed from irradiation. Under the assumption of hydrostatic equilibrium, the Coriolis force could lead to a moderate increase of the mass transfer rate by pushing the gas in the vertical direction at the $L_1$ point, but only during the initial phases of the outburst (about 15 -- 20 orbital periods). We conclude that the Coriolis force does not prevent a flow from the heated regions of the secondary towards the $L_1$ region, at least during the initial phase of an outburst, but the resulting increase of the mass transfer rate is moderate, and it is unlikely to be able to account for the duration of long outbursts.
