It is well known that sheared plasma flows can be built up both in ast
rophysical environments as well as in laboratory dusty plasmas. Our ob
jective here is to understand the coupling of velocity gradient energy
to electrostatic and electromagnetic waves in nonuniform dusty magnet
oplasma. For this purpose, we employ the multi-fluid dusty plasma mode
l and derive the relevant nonlinear equations for low-frequency (in co
mparison with the ion gyrofrequency) waves in the presence of sheared
plasma hows. Linear dispersion relations are derived and analyzed. It
is found that both the electrostatic and electromagnetic waves are dri
ven by sheared plasma flows. Furthermore, the newly derived mode coupl
ing equations provide the possibility of self-organized and chaotic st
ates in dusty plasmas. The results of our investigation should be help
ful in understanding the properties of dusty plasma microturbulence wh
en sources and sinks are simultaneously present.