Particular Solutions for Slow Viscous Flows Close to Solid Body Rotation. Analytic Discussion and Examples

摘要

Particular solutions for slow viscous flows close to solid body rotation are found by product hypotheses which lead to two different eigenvalue problems. The adjoint equations and orthogonality conditions are derived. For high values of the Ekman number some of the particular solutions can be interpreted as the contribution of the Ekman layer. A simplified differential equation is derived for the interior of the flow field; it is valid if the Ekman number is large. The effect of the Ekman layer is taken into account by modified boundary conditions. For a problem studied by Stewartson, the solution is expressed in terms of both kinds of particular solutions. Also discussed are flow patterns in which the formation of striation is inhibited. Further examples show flow fields with perturbation introduced along cylindrical boundaries. Examples using the complete solutions are given; certain discontinuities of the schematic flow fields are smoothed out. Also discussed is the relation between these solutions and a solution with different boundary conditions due to Morrison and Morgan. (Author)