The Problems in Terms of Stresses of Diffusion-Vortex Class in Infinite Rigid Viscoplastic Space

Abstract

The statements and exact self-similar solutions of diffusion-vortex problems in terms of stresses simulating a nonstationary one-dimensional shear in some curvilinear orthogonal coordinate systems of a two-constant stiff-viscous plastic medium (Bingham body) are analyzed. Such problems include the diffusion of plane and axisymmetric vortex layers, as well as the diffusion of avortex filament. The shear occurs in regions of unlimited space expanding with time with a pre-unknown boundary, and a possible way of specifying an additional condition at infinity is described. A generalized vortex diffusion is introduced into consideration, containing a formulation with several parameters, including the order of the singularity peculiarities at zero. Self-similar solutions are constructed in which the order of the singularity corresponds to or does not correspond to the type of shift in the selected coordinate system.