  Disk accretion at high rate onto a white dwarf or a neutron star has been
suggested to result in the formation of a spreading layer (SL) - a belt-like
structure on the object's surface, in which the accreted matter steadily
spreads in the poleward (meridional) direction while spinning down. To assess
its basic characteristics we perform two-dimensional hydrodynamic simulations
of supersonic SLs in the relevant morphology with a simple prescription for
cooling. We demonstrate that supersonic shear naturally present at the base of
the SL inevitably drives sonic instability that gives rise to large scale
acoustic modes governing the evolution of the SL. These modes dominate the
transport of momentum and energy, which is intrinsically global and cannot be
characterized via some form of local effective viscosity (e.g.
$\alpha$-viscosity). The global nature of the wave-driven transport should have
important implications for triggering Type I X-ray bursts in low mass X-ray
binaries. The nonlinear evolution of waves into a system of shocks drives
effective re-arrangement (sensitively depending on thermodynamical properties
of the flow) and deceleration of the SL, which ultimately becomes transonic and
susceptible to regular Kelvin-Helmholtz instability. We interpret this
evolution in terms of the global structure of the SL and suggest that mixing of
the SL material with the underlying stellar fluid should become effective only
at intermediate latitudes on the accreting object's surface, where the flow has
decelerated appreciably. In the near-equatorial regions the transport is
dominated by acoustic waves and mixing is less efficient. We speculate that
this latitudinal non-uniformity of mixing in accreting white dwarfs may be
linked to the observed bipolar morphology of classical novae ejecta.
