  The 2D hydrodynamic model for a dust cloud confined in an axisymmetric
toroidal system volumetrically driven by an unbounded streaming plasma is
further extended systematically for different aspect-ratio of the bounded dust
domain and a wide range of the kinematic viscosity. This work has demonstrated
the interplay between inertial and diffusive transport processes for the
structural changes of steady dust flow from symmetric into asymmetric nature in
higher Reynolds number (Re) regimes where flow streamlines turn more circular
and the structural bifurcation takes place through a threshold parameter. In
agreement with many experimental observations, the steady vortex structure in
highly nonlinear (i.e., high Re) regime is characterized by the critical
transition into a new self-similar multiple co-rotating vortices, along with
circular core region of single characteristics size and surrounded by strongly
sheared layers filled with weak vortices near the boundaries. It is further
revealed that the core region persists for a wide range of system parameters in
the nonlinear regime and its characteristic size is mainly determined by the
smallest distance between the confining boundaries. The threshold parameter,
the vortex size, the strength, and the number of the self-similar co-rotating
vortices mainly depend on the aspect-ratio of the bounded dust domain. These
nonlinear solutions provide insight into the phenomena of the structural
transition and coexistence of self-similar steady co-rotating vortices in dusty
plasma experiments as well as many relevant complex driven-dissipative natural
flow systems.
