  Analysis of driven dust vortex flow is presented in a weakly magnetized
plasma. The 2D hydrodynamic model is applied to the confined dust cloud in a
non-uniform magnetic field in order to recover the dust vortex flow driven in a
conservative force field setup, in absence of any non-conservative fields or
dust charge variation. Although the time independent electric and magnetic
fields included in the analysis provide conservative forcing mechanisms, when
the a drift based mechanism, recently observed in a dusty plasma experiment by
[M. Puttscher and A. Melzer, Physics of Plasmas, 21,123704(2014)] is
considered, the dust vortex flow solutions are shown to be recovered. We have
examined the case where purely ambipolar electric field, generated by
polarization produced by electron E*B drift, drives the dust flow. A sheared
E*B drift flow is facilitated by the magnetic field gradient, driving the
vortex flow in the absence of ion drag. The analytical stream-function
solutions have been analyzed with varying magnetic field strength, its gradient
and kinematic viscosity of the dust fluid. The effect of B field gradient is
analyzed which contrasts that of E field gradient present in the plasma sheath.
