The vortex structures in a cloud of electrically suspended dust in a streaming plasma constitutes a driven system with a rich nonlinear flow regime. Experimentally recovered toroidal formations of this system have motivated study of its volumetrically driven-dissipative vortex flow dynamics using two-dimensional hydrodynamics in the incompressible Navier-Stokes regime. Nonlinear equilibrium solutions are obtained for this system where a nonuniformly driven two-dimensional dust flow exhibits distinct regions of localized accelerations and strong friction caused by stationary fluids at the confining boundaries resisting the dust flow. In agreement with observations in experiments, it is demonstrated that the nonlinear effects appear in the limit of small viscosity, where the primary vortices form scaling with the most dominant spatial scales of the domain topology and develop separated virtual boundaries along their periphery. This separation is triggered beyond a critical dust viscosity that signifies a structural bifurcation. Emergence of uniform vorticity core and secondary vortices with a newer level of identical dynamics highlights the applicability of the studied dynamics to gigantic vortex flows, such as the Jovian great red spot, to microscopic biophysical intracellular activity.
Flow structure of a dust medium electrostatically suspended and confined in a plasma presents a unique setup where the spatial scale of a volumetric drive by the plasma flow might exceed that of the boundaries confining the dust. By means of a formal implementation of a two-dimensional hydrodynamic model to a confined dust flow and its analytic curvilinear solutions, it is shown that the eigenmode spectrum of the dust vortex flow can lose correlations with the driving field even at the low dust Reynolds numbers as a result of strong shear and finer scales introduced in the equilibrium dust vorticity spectrum by the boundaries. While the boundary effects can replace the desired turbulent processes unavailable in this regime, the shear observable in most of the dust vortex flows is identified to have a definite exponent of dependence on the dust viscosity over a substantially large range of the latter. These results and scalings allow quantification of the notion of dusty plasma medium as a paradigm for a wide range of natural flow processes having scales inaccessible to ordinary laboratory experiments.
Dynamics of an isothermally driven dust fluid is analyzed which is confined in an azimuthally symmetric cylindrical setup by an effective potential and is in equilibrium with an unconfined sheared flow of a streaming plasma. Cases are analyzed where the confining potential constitutes a barrier for the driven fluid, limiting its spatial extension and boundary velocity. The boundary effects entering the formulation are characterized by applying the appropriate boundary conditions and a range of solutions exhibiting single and multiple vortex are obtained. The equilibrium solutions considered in the cylindrical setup feature a transition from single to multiple vortex state of the driven flow. Effects of (i) the variation in dust viscosity, (ii) coupling between the driving and the driven fluid, and (iii) a friction determining the equilibrium dynamics of the driven system are characterized.
A 2D hydrodynamical model is developed and analyzed for the steady state of a driven-dissipative dust clouds confined in an azimuthally symmetric toroidal system which is in dynamic equilibrium with background unbounded streaming plasma. Its numerical solution not only confirms the analytical structure of the driven dust vortex flow in linear limit as reported in previous analysis, but also shows how the dust vortices are strongly affected by the nonlinear convection of the flow itself. Effects of various system parameters including external driving field and Reynolds number (Re) are investigated within the linear to nonlinear transition regime 0.001 ≤ Re < 50. In agreement with various relevant experimental observations, the flow structure which is symmetric around center in the linear regime begins to turn asymmetric in the nonlinear regime. The equilibrium structure of dust flow is found to be influenced mainly by the dissipation scales due to kinematic viscosity, ion drag, and neutral collision in the nonlinear regime, whereas in the linear regime, it is mainly controlled by the external driving field and the confining boundaries.
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.
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