Recent studies of nonmodal phenomena in two-component plasma flows revealed that the velocity shear induces a number of new effects both in electrostatic and magnetized shear flows. It can be expected that dusty plasmas also host shear-modified and shear-induced modes of collective behavior, which may be found by means of the nonmodal approach and which are inaccessible by means of the standard normal mode analysis. In this paper, considering the simple electrostatic dusty plasma case, a general mathematical formalism is developed for studying how velocity shear affects the evolution of dust-acoustic waves (DAWs) and ion-acoustic waves (IAWs). In the limiting (very low-frequency) case when Boltzmann distributions are used both for the electrons and the ions it is found that the velocity shear enables the extraction of kinetic energy of the background flow by the dust-acoustic waves. It is also shown that the velocity shear leads to the appearance of a new collective mode of the dust particles-shear dust vortices. In the general case it is demonstrated that the velocity shear couples DAWs and IAWs and under suitable conditions may cause their mutual transformation into each other. The flow also sustains shear ion-dust vortices-nonperiodic patterns, which may eventually acquire oscillating features and generate both DAWs and IAWs. The inverse regime, which is called evanescence of acoustic waves, can also occur: the initial blend of DAWs and IAWs can fade away degenerating into the nonperiodic, evanescent perturbation. (C) 2000 American Institute of Physics. [S1070-664X(00)04108-2].