Structural changes of self-organized vortices in Jupiter atmospheres such as Great Red Spot (GRS) and White Ovals are demonstrated using an electrostatically bounded charged dust cloud in an unbounded streaming plasma as the prototype for various driven-dissipative complex flow systems in nature. Using a 2D hydrodynamic model, the steady state flow solutions are obtained for the volumetrically driven dust cloud in a bounded domain of aspect-ratio of 1.5 relevant to the current size of GRS and a driving sheared ion flow similar to the part of zonal jets streaming through the GRS. These nonlinear solutions reveal many similar characteristic features between the steadily driven dust circulation in laboratory experiments and the vortices in Jupiter atmosphere. Starting from the continuous structural changes, the persistence of high-speed collar ring around the quiescent interior of uniform vorticity of GRS and White Ovals are interpreted as a consequence of changes in internal properties related to kinematic viscosity rather than the driving fields. This the analysis also sheds light on the roles of driving field, boundaries, and dynamical parameters regime in determining the characteristic size, the strength, the circulating direction, and the drift of the vortices in Jupiter atmosphere and other relevant driven-dissipative flow systems in nature.