  We perform a detailed analytical and numerical study of the dynamics of
perturbations (vortex/aperiodic mode, Rossby and spiral-density waves) in 2D
compressible disks with a Keplerian law of rotation. We draw attention to the
process of spiral-density wave generation from vortices, discussing, in
particular, the initial, most peculiar stages of wave emission. We show that
the linear phenomenon of wave generation by vortices in smooth (without
inflection points) shear flows found by using the so-called non-modal approach,
is directly applicable to the present case. After an analytical non-modal
description of the physics and characteristics of the spiral-density wave
generation/propagation in the local shearing-sheet model, we follow the process
of wave generation by small amplitude coherent circular vortex structures, by
direct global numerical simulation, describing the main features of the
generated waves.
