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The strongly coupled dusty plasma has often been modelled by the GeneralizedHydrodynamic (GHD) model used for representing visco-elastic fluid systems. Theincompressible limit of the model which supports transverse shear wave mode isstudied in detail. In particular dipole structures are observed to emittransverse shear waves in both the limits of sub and super - luminarpropagation, where the structures move slower and faster than the phasevelocity of the shear waves, respectively. In the sub - luminar limit thedipole gets engulfed within the shear waves emitted by itself, which thenbackreacts on it and ultimately the identity of the structure is lost. However,in the super - luminar limit the emission appears like a wake from the tailregion of the dipole. The dipole, however, keeps propagating forward withlittle damping but minimal distortion in its form. A Poynting like conservationlaw with radiative, convective and dissipative terms being responsible for theevolution of W , which is similar to `enstrophy' like quantity in normalhydrodynamic fluid systems, has also been constructed for the incompressibleGHD equations. The conservation law is shown to be satisfied in all the casesof evolution and collision amidst the nonlinear structures to a great accuracy.It is shown that monopole structures which do not move at all but merelyradiate shear waves, the radiative term and dissipative losses solelycontribute to the evolution of W. The, dipolar structures, on the other hand,propagate in the medium and hence convection also plays an important role inthe evolution of W.

physics of plasmas

Sub and super-luminar propagation of structures satisfying Poynting like  theorem for incompressible GHD fluid model depicting strongly coupled dusty  plasma medium