Domains with Boundaries

  • Paul K. Newton
Part of the Applied Mathematical Sciences book series (AMS, volume 145)


In this chapter we consider the dynamics of 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:
$$u \cdot n = 0{|_{\partial D}}$$
• The presence of boundaries can break symmetries that would otherwise exist and thus reduce the number of conserved quantities.


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

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • Paul K. Newton
    • 1
  1. 1.Department of Aerospace and Mechanical Engineering and Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

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