Holichenko O. Mechanisms of three-dimensional mixing of a viscous fluid in a finite cylinder

The thesis is devoted to the study of the mechanisms of three-dimensional mixing of a viscous, homogeneous, incompressible fluid at small Reynolds numbers in a finite circular cylinder with periodic motion of the cylinder boundaries. Analytical solutions of the boundary value problem of three-dimensional stationary motion of a viscous, homogeneous, incompressible fluid in a finite circular cylinder at small Reynolds numbers for new, previously not considered boundary conditions are obtained. In order to be used for practical calculations, the convergence of analytical solutions to the boundary value problem of three-dimensional stationary motion of a viscous, homogeneous, incompressible fluid in a finite circular cylinder at small Reynolds numbers is improved by finding the asymptotic behavior of series coefficients by which the fluid inside the cylinder is expressed. Using these results, the influence of different parameters, in particular the height of the cylinder and the period of switching the velocity at the cylinder boundary on the mixing of the liquid inside the cylinder is analyzed.