In this paper the foundation is layed for the nonmodal investigation of velocity shear induced phenomena in a differentially rotating flow of a dusty plasma. The simplest case of nonmagnetized flow is considered. It is shown that, together with the innate properties of the dusty plasma, the presence of differential rotation, Coriolis forces, and self-gravity casts a considerable richness on the nonmodal dynamics of linear perturbations in the flow. In particular: (i) dust-acoustic waves acquire the ability to extract energy from the mean flow and (ii) shear-induced, nonperiodic modes of collective plasma behavior—shear-dust-acoustic vortices—are generated. The presence of self-gravity and the nonzero Coriolis parameter (“epicyclic shaking”) makes these collective modes transiently unstable. ©2000 American Institute of Physics.