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Position of line vortex from Stream function

  1. May 16, 2007 #1
    1. The problem statement, all variables and given/known data

    So, the problem is 4 line vortices in a 2-d square. All have the same strength. Im asked to find the motion of the vortices in the flow of the others. Meaning, each vortex moves in the flow of the other three. I know the correct solution should be just a circular pattern but i can't seem to make it work out.

    2. Relevant equations

    I'm 'given' the stream function of a line vortex and allowed to set 'a' (the distance of each side on the square) to anything.

    3. The attempt at a solution

    So I can plot the correct stream lines for all four vorticies at once.

    Then, excluding the vortex whose motion im looking for, i find dpsi/dy = u and dpsi/dx = v.

    From there, I should be able to setup and solve dx/dy = u and dy/dt = v as ODE's, correct?

    I'm using a working runga kutta solver in matlab but the results are incorrect (a line y=x).
  2. jcsd
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