Driven dust vortex characteristics in plasma with external transverse and weak magnetic field

The two-dimensional hydrodynamic model for bounded dust flow dynamics in plasma is extended for analysis of driven vortex characteristics in presence of external transverse and weak magnetic field (${\bf B}$) in a planner setup and parametric regimes motivated by recent magnetized dusty plasma (MDP) experiments. This analysis has shown that shear in the ${\bf B}$ can produce a shear internal field (${\bf E_a}$) in between electrons and ions due to the ${\bf E}\times {\bf B}$ and ${\nabla {\bf B}}\times {\bf B}$-drifts that cause rotation of dust cloud levitated in the plasma. The flow solution demonstrates that neutral pressure decides the dominance between the ions-drag and the ${\bf E_a}$-force. The shear ions-drag generates an anti-clockwise circular vortical structure, whereas the shear ${\bf E_a}$-force is very localized and gives rise to a clockwise $D$-shaped elliptical structure which turns into a meridional structure with decreasing ${\bf B}$. Effect of system parameters including the strength of ${\bf B}$ by varying its magnitude and shear mode numbers and the sheath field are analyzed within the weak MDP regime, showing noticeable changes in the flow structure and its momentum. In the parametric regime of high pressure and lower ${\bf B}$, the ${\bf E_a}$-force becomes comparable or dominant over the ion drag and peculiar counter-rotating vortex pairs are developed in the domain. Further, when the ${\bf B}$ is flipped by $180^0$-degree, both the drivers act together and give rise to a single strong meridional structure, showing the importance of ${\bf B}$-direction in MDP systems. It further discussed similar elliptical/meridional structures reported in several MDP experiments and relevant natural driven-dissipative flow systems.