It is shown that purely damped convective cell modes acquire a real frequency in the presence of static charged dust grains in a nonuniform magnetized dusty plasma. The frequency of the two‐dimensional mode is induced by the plasma density gradient and corresponds to charge density waves arising out of the plasma non‐neutrality. The dynamics of weakly interacting finite‐frequency convective cell modes is governed by the generalized Navier–Stokes equation. The presence of the new term arising from the dust inhomogeneity in the latter provides the possibility of a two‐dimensional dipolar vortex solution in dusty plasmas.