Gary
GaryVasco
Posts: 3,352 
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Post by Gary on Jan 7, 2018 22:54:35 GMT
Vasco, I am puzzled by the index number +2 in the dipole of figure [5]. If we draw a few Vs on a simple curve that doesn't cross S, it appears that Vs must rotate clockwise as they cross the curve on the left field of the dipole and rotate counter clockwise as they cross the curve on the right field. I would have expected the rotations to add to zero. Can you explain the index of +2? The attached plot is intended to illustrate the rotations. vector_field_rotation_auto.pdf (66.73 KB) Gary |
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Post by Admin on Jan 8, 2018 7:22:49 GMT
Gary
+2 seems correct to me:
If you start at the N pole of the ellipse with V pointing south along the streamline, then as you move west into the NW quadrant of the ellipse, V rotates anticlockwise so that when you get to the westernmost tip of the ellipse, V is pointing North.
Then as you continue into the SW quadrant of the ellipse, towards the south pole, V continues to rotate anticlockwise and when you reach the south pole, V is again pointing south having made a complete revolution anticlockwise as you traverse the western half of the ellipse.
Now, as you continue along the ellipse, into the SE quadrant heading towards the easternmost tip of the ellipse, V continues to rotate anticlockwise, and when you reach the easternmost tip of the ellipse you are pointing north.
Finally, as you head back towards the north pole, you rotate anticlockwise, so that when you reach the north pole again you are pointing south again, and so you have made a total of 2 anticlockwise rotations.
Vasco
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Gary
GaryVasco
Posts: 3,352
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Post by Gary on Jan 8, 2018 15:21:14 GMT
Gary +2 seems correct to me: If you start at the N pole of the ellipse with V pointing south along the streamline, then as you move west into the NW quadrant of the ellipse, V rotates anticlockwise so that when you get to the westernmost tip of the ellipse, V is pointing North. Then as you continue into the SW quadrant of the ellipse, towards the south pole, V continues to rotate anticlockwise and when you reach the south pole, V is again pointing south having made a complete revolution anticlockwise as you traverse the western half of the ellipse. Now, as you continue along the ellipse, into the SE quadrant heading towards the easternmost tip of the ellipse, V continues to rotate anticlockwise, and when you reach the easternmost tip of the ellipse you are pointing north. Finally, as you head back towards the north pole, you rotate anticlockwise, so that when you reach the north pole again you are pointing south again, and so you have made a total of 2 anticlockwise rotations. Vasco Vasco, Thank you. I see it now. Gary |
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