The *N*-Vortex Problem
pp 117-138 |
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# Domains with Boundaries

Chapter

## Abstract

In this chapter we consider the dynamics of • The presence of boundaries can break symmetries that would otherwise exist and thus reduce the number of conserved quantities.

*N*vortices in planar domains with solid boundaries. The domains could be closed, simply connected regions in the plane (e.g., interior of a unit circle), closed, multiply connected regions (e.g., interior of an annular region), or they could be unbounded but containing a solid boundary (e.g. upper half-plane or corner geometries). This problem differs considerably from that described in the previous chapter for two important reasons: • On the solid boundary*∂D*the condition of no fluid penetration must be imposed:$$u \cdot n = 0{|_{\partial D}}$$

(1)

## Keywords

Complex Potential Solid Boundary Point Vortex Vortex Motion Circular Domain
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## Copyright information

© Springer-Verlag New York, Inc. 2001