Dynamic behavior of impurities in the flow field of a stratified viscous incompressible fluid

V. A. Galkin<sup>ab

a</sup> Surgut Branch of Scientific Research Institute for System Analysis of the National Research Centre “Kurchatov Institute”, Surgut, Russian Federation
^b Surgut State University, Surgut, Russian Federation

Abstract: We studied the structure of the solution to the impurity transport equation under the influence of a vortex-type solution of the Navier–Stokes equations for incompressible fluid flow in planes orthogonal to a distinguished axis, referred to as the "well". We described the structure of these solutions in the vicinity of the well, which arises due to rotational motion in the invariant flow planes. Our analysis shows that the dynamics of impurities in such flows can generate a spatial structure resembling cavitation, observed in high-speed motion along the selected axis. This phenomenon results in the formation of a narrow region of impurity dilution. We also provided examples demonstrating the formation of such axially symmetric structures.

Keywords: incompressible fluid equations, exact solutions of the Navier-Stokes system, transport equation.