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.
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