  Disk accretion onto weakly magnetized astrophysical objects often proceeds
via a boundary layer that forms near the object's surface, in which the
rotation speed of the accreted gas changes rapidly. Here we study the initial
stages of formation for such a boundary layer around a white dwarf or a young
star by examining the hydrodynamical shear instabilities that may initiate
mixing and momentum transport between the two fluids of different densities
moving supersonically with respect to each other. We find that an initially
laminar boundary layer is unstable to two different kinds of instabilities. One
is an instability of a supersonic vortex sheet (implying a discontinuous
initial profile of the angular speed of the gas) in the presence of gravity,
which we find to have a growth rate of order (but less than) the orbital
frequency. The other is a sonic instability of a finite width, supersonic shear
layer, which is similar to the Papaloizou-Pringle instability. It has a growth
rate proportional to the shear inside the transition layer, which is of order
the orbital frequency times the ratio of stellar radius to the boundary layer
thickness. For a boundary layer that is thin compared to the radius of the
star, the shear rate is much larger than the orbital frequency. Thus, we
conclude that sonic instabilities play a dominant role in the initial stages of
nonmagnetic boundary layer formation and give rise to very fast mixing between
disk gas and stellar fluid in the supersonic regime.
