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Navier Stokes: Spherical form

  1. Jan 2, 2004 #1

    I'm trying to understand how to convert the cartesian form of the N-S equation to cylinderical/spherical form. Rather than re-derive the equation for spherical/cylindrical systems, I am trying to directly convert the cartesian PDE.

    I'm ok with converting the d/dx and d2/dx2 terms. What I am struggling with a little, is the v_x, v_y and v_z terms which represent velocity in the x, y and z directions respectively.

    Start simple with cylindrical...

    Any idea on how to represent v_x and v_y in terms of v_r and v_theta?

    I make v_r to be v_x / cos(theta). But can't see how to find v_theta. Any help is much appreciated.


  2. jcsd
  3. Jan 5, 2004 #2
    Any ideas at all?


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