page_title: Elementary flow
section_title: Two Dimensional vortex line
hierarchical_section_title: Elementary flow / Two Dimensional vortex line
caption_attribution_description: English: Spinning Vortex
context_page_description: Elementary flow is a collection of basic flows from which is possible to construct more complex flows by superposition. Some of the flows reflect specific cases and constraints such as incompressible, irrotational or both as in the case of Potential flow.
context_section_description: This is the case of a vortex filament rotating at constant speed, there is a cylindrical symmetry and the problem can be solved in the orthogonal plane.
  Dual to the case above of line sources, Vortex lines play the role of monopoles for irrotational flows.
  Also in this case the flow is also both irrotational and incompressible and therefore a case of Potential flow.
  This is characterized by a cylindrical symmetry:
  Where the total circulation is constant for every closed line around the central vortex 
  and is zero for any line not including the vortex.
  Therefore,
  This is derived from a stream function
  or from a potential function
  Which is dual to the previous case of a line source
caption: Dashed Potential flow streamlines for an ideal vertical vortex line
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