  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 replaced 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.
