Steady Stokes flow in an annular cavity

This paper addresses a general analytical method of superposition for the study of two-dimensional creeping flows in a wedge-shaped cavity arb, ||0 caused by tangential velocities of its curved walls. The method is illustrated by several numerical examples; the rate of convergence and the accuracy of fulfilling the boundary conditions are investigated. The main objective is to demonstrate the advantages of the method of superposition when analysing streamline patterns and the velocity-field distribution in the whole domain, including the Moffatt eddies near corner points. The equations for the positions of the stagnation and separation points are written analytically. The streamline patterns for uniform velocities at the top and the bottom walls are shown graphically. These patterns represent the transition from the corner eddies into internal eddies

Motion of a two-dimensional monopolar vortex in bounded rectangular domain

In this paper we describe results of a study of the two-dimensional motion of a distributed monopolar vortex in a viscous incompressible fluid in a bounded rectangular domain with free-slip and no-slip boundary conditions. In the case of free-slip walls the motion of the vortex center can be satisfactorily modelled by a single point vortex in an inviscid fluid. Comparison of the results of both models reveals a good quantitative agreement for the trajectories of the vortex centers and of the period of one revolution around the center of the domain, for moderate viscous effects (Re=1000 and more). In a domain with no-slip walls the distributed monopolar vortex moves to the center of the domain along a curved but not smooth trajectory due to the interaction of the monopole and the wall-induced vorticity

Mixing in the Stokes flow in a cylindrical container

Kinematic features of three-dimensional mixing by advection of passive particles in time-periodic flows are the primary subject of this study. A classification of periodic points, providing important information about the mixing properties of a flow, is presented, and the dynamics of the Poincare map in the vicinity of periodic points is analysed for all identified types. Three examples of Stokes flow in a finite cylindrical cavity with discontinuous periodic motion of its end walls are used to illustrate the determination of both periodic lines and isolated periodic points in the flow domain. The stable and unstable manifolds of points on the periodic lines create two surfaces in the flow. A numerical technique based on tracking of a material surface is presented to study the manifold surfaces and their intersections. It is illustrated with numerical examples that flows with periodic lines possess only quasi-two-dimensional mechanisms of chaotic advectio