  Disk accretion onto weakly magnetized objects possessing a material surface
must proceed via the so-called boundary layer (BL) -- a region at the inner
edge of the disk, in which the velocity of accreting material abruptly
decreases from its Keplerian value. Supersonic shear arising in the BL is known
to be conducive to excitation of acoustic waves that propagate into the
accretor and the disk, enabling angular momentum and mass transport across the
BL. We carry out a numerical exploration of different wave modes that operate
near the BL, focusing on morphological characteristics of the modes in the
innermost parts of accretion disk. Using a large suite of simulations covering
a broad range of Mach numbers (of the supersonic shear flow in the BL), we
provide accurate characterization of the different types of modes, verifying
their properties against analytical results, when available. We discover new
types of modes, in particular, global spiral density waves launched by vortices
forming in the disk near the BL as a result of the Rossby wave instability;
this instability is triggered by the vortensity production in that region
caused by the nonlinear damping of acoustic waves. Azimuthal wavenumbers of the
dominant modes that we observe appear to increase monotonically with the Mach
number of the runs, but a particular mix of modes found in a simulation is
mildly stochastic. Our results provide a basis for better understanding of the
angular momentum and mass transport across the BL as well as the emission
variability in accreting objects.
