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Vector field curvature in the complex plane

  1. Apr 9, 2012 #1
    Hey all,

    I have a vector field described by a complex potential function (so I have potential lines and streamlines). I am looking for a way to express its curvature at every point, but I can't find such a formula in my books. I have searched in wikipedia and I read that the way to define it in cartesian coordinates is through a parametric curve, but I'm not sure how I should go about it in the complex plane.

    If anyone can give me a pointer on how to derive the curvature of the field or to relevant reading material, I would be grateful :biggrin:
     
  2. jcsd
  3. Apr 9, 2012 #2

    lavinia

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    I am not sure what you mean by the curvature of a vector field.

    Do you mean the curvature of the potential and stream lines or do you mean the curvature of the conformal metrics determined by the potential?
     
  4. Apr 9, 2012 #3
    You are right, I wasn't clear, I mean the curvature of the potential and stream lines!
     
  5. Apr 10, 2012 #4
    Shameless bump :biggrin:
     
  6. Apr 10, 2012 #5

    lavinia

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    I haven't had a chance to figure out if there is a general description but I would try working out some simple examples first - e.g. with algebraic functions in the plane.

    You need to parameterize the curves u = constant, and v = constant by arclength then differentiate the unit length tangent vector.
     
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