It is shown that sheared plasma flows can generate nonthermal electrostatic waves in a magnetized dusty electron–positron plasma. Linearly excited modes attain large amplitudes and start interacting among themselves. Nonlinearly coupled modes self-organize in the form of coherent vortices comprising a vortex chain and a double vortex. Conditions under which the latter appear are given. The relevance of our investigation to space, astrophysical, and laboratory plasmas is pointed out.