Question: Problem 1 The data at the end of this document measure vectors tangent to a sphere, rounded. Select any closed curve with a positive arc

Problem 1 The data at the end of this document

Problem 1 The data at the end of this document measure vectors tangent to a sphere, rounded. Select any closed curve with a positive arc length on the surface of the sphere. Estimate the circulation of the vector field around your curve. Estimate the net outward flow of the vector field around your curve. Optionally, the original data are available at [1, Source Data Fig. 2). zonal velocity -60. -50. . -40. -30. - 20. -10. 0. 10. 20. 30. 40. . 50. 60. 23. 3.5 3.2 3. 3 3.2 3.6 2.4 2.7 2.1 2.9 3.6 3.5 1.9 -3.4 22 4.4 3.8 4. 4.2 3.3 1.7 1.9 2.5 3.1 5. 6.6 7.6 3.4 21. . 3.9 3.5 3.4 3.8 2.9 1.4 1.4 2.4 2.8 4.3 5.5 6.7 3. 20. 0.7 1.9 2.4 2.1 0.8 0.3 1. 2.4 4.4 5.2 4.9 4.5 3.4 19. . 1.2 1.3 1.2 -0.2 -0.8 0. 0.9 2.2 3.3 3.2 2.6 0.8 2. 18. 0.4 0. . -0.3 -1.7 -2.8 -1.5 -0.1 1.8 2.8 1.7 1.7 -0.9 1.1 17. 0.4 -0.7 -1. -2.4 -3.4 -2.6 -1.7 -0.3 -0.2 -1.3 -0.3 -0.4 -0.3 16. -1.6 -1.9 -1.8 -3.4 -4.1 -4.4 -2.6 -2 -0.8 -1.4 0. 0 0.1 -2.2 15. -3. -3.5 -2.5 -2.5 -2.6 -3.3 -2.7 14. -2. -1.9 -1. -0.5 -0.3 -1.1 -0.6 -1. -0.8 -1.6 - 1.6 -1.5 0.2 13 -1.6 -0.8 0.1 1.8 1.2 1.3 1. 2.1 0.2 -0.8 -2.2 -1.1 0.1 12. -0.7 1.4 2.1 2.6 1.6 1.9 2. 3.6 3.1 2.4 0.3 0.6 0.3 11. -0.8 1. 1.1 1.8 1.3 2.9 2.5 3.9 2.6 2.7 1.1 1.7 -2. 10. 0.4 0.9 1.2 2.3 2.5 3.2 2. 2.4 2.4 1.5 0.5 1.2 1 1. 9. 0.7 0.7 0.4 1.7 2.1 3.3 2.1 2.1 1.2 -0.1 -0.6 0.1 1.9 8. 0. 0.7 0.6 1.6 1.3 2.1 1.5 1. 0.2 -1. -0.9 -1. 1.5 7. -0.9 -0.2 0.1 0.5 0.3 1. 1.4 -0.1 -1.3 -1.6 -0.3 -0.8 0.1 6. -1.5 -1.3 -0.5 0. 0.3 -0.6 -0.1 -1.2 -2.6 -3.4 -3. -1.4 0.2 . 5. -0.5 -1.6 -2.9 -3.6 -4. -4.5 -2.6 -3.4 -3.9 -5.3 -4.1 -2.3 -1.5 4. -1.7 -2.9 -3.7 -5. -5.2 -5.1 -3.9 -4.4 -4.7 -4.6 -3.3 -3.2 -2. 3. -2.1 -2.8 -3.6 -5.1 - 6.2 -4.8 -4.7 -4.4 -4.6 -2.4 -1. -1.3 -0.6 2. -1.3 -2.6 -2.2 -2.3 0.8 0.6 -2.7 -4.8 -5.2 -2.2 -2.6 -3.4 1.1 1. -0.3 -0.1 -1.1 -0.2 2.7 2.2 -0.8 -2.8 -2.2 -1.3 -3.9 -4.6 -1.6 . 0. 2.4 2. 1. 1.2 4.8 3.6 2.1 -1.2 0.1 0.4 -1.5 -3.3 -4.6 -2.9 -2.9 -2.9 -1.4 -0.3 -1.1 meridional velocity -60. -50. -40. - 30. -20. -10. 0. 10. 20. 30. 40. 50. 60. 23. -1.7 -0.9 -0.3 1.4 3.1 1.4 0.1 -2. -3.2 -4. -5.3 -4.5 -3.7 22. 0.3 1.5 1.8 3.2 3.2 1.2 -0.4 -2.7 -4.4 -5.6 -6.4 -5.9 -5.4 21. 2.2 2.7 2.8 3.4 2.8 0.9 -0.9 -2.8 -4.4 -5.4 -5. -3.9 -2.8 20. 1.7 2. 2.2 2.4 1.4 0. -1.7 -3.7 -5.5 -6.4 -4.3 -2.2 0. 19. 1.5 1.5 1.9 1.2 1.1 -0.6 -1.8 -3.4 -4.6 -4.4 -3. -0.7 0.8 18. 1.6 1.5 2. 1. . 1. -0.3 -1.9 -3.7 -4.4 -3.7 -2.3 -1. 0.4 17. 0.6 0.4 1.7 0.9 0.8 -0.2 -1.4 -1.9 -2.3 -1.5 -0.4 1.3 2.1 16. -0.7 -1.4 0.3 -0.1 0. -0.1 -0.6 -0.6 -1.9 -1.6 -0.4 2.9 4.9 15. -3. -3.5 -1.7 -1.1 -0.6 -0.5 0.1 0.8 0.3 0. 0 1.4 4.6 5.8 14. -3.8 -4.7 -2.9 -1.6 -0.7 -0.9 -0.3 0.1 0.3 1. . 3. 4.9 3.6 13. -5.1 -6.5 -4.8 -3.1 -1.7 -1.4 -0.5 0.7 2.3 3.4 4.8 4.6 2.5 12. -5.1 -6.3 -5.3 -4.3 -2.7 -1.5 -0.1 1.2 2.9 4.3 5.5 5.6 3.7 11. -5.4 -6.9 -6.5 -5.6 -3.6 -1.3 0.5 1.8 3.1 3.7 4.5 5.1 5.9 10. -5.4 -5.8 -5.2 -4.7 -3.5 -1.5 0.1 1.1 2.5 3.2 4.2 3.6 9. -4.3 -4.5 -4. -3.8 -3.3 -1.8 -0.3 0.4 1.4 2.2 3.3 1.8 0.8 8. -3.2 -2.2 -1.6 -1.4 -1.8 -1 -0.6 0. . 0.2 1.4 2.5 0.9 0. . 7. -1.8 -0.5 -0.2 0.1 -0.2 -0.1 -0.4 -0.6 -1.3 -0.2 0.7 0.3 -0.1 6. -1.5 0.6 1.1 2.2 1.6 0.9 -0.6 -1.5 -2.6 -1.3 -0.1 0.3 -1.4 5. -1.1 1.3 1.9 2.6 1.9 0.2 -0.7 -1.3 -1.6 -0.8 0.2 0.6 -1.7 4. -1.6 0.4 1. 2.2 1.5 0.7 0.1 -0.3 -0.7 0.9 2.8 3.5 0.9 3. -2.5 -1.3 -0.3 0.6 1. 0.6 0.7 1.6 1.5 2.3 3. 3.6 2.9 2. -3.5 -2.7 -2.3 -0.7 0 0.3 0.5 1.6 2.1 2.7 3.4 4.1 2.5 1. 1 - 3.5 -2.8 -2.4 -0.9 0.6 0.4 -0.1 0.4 1.1 0.6 1. 1.1 1.8 0. . -3.7 -2.9 -2.3 -0.2 1.1 0.4 -0.5 -1.3 -1.7 -2. -2.2 -1.7 -0.9 2.4 v (23,60) =(-3.4, -3.7) Problem 1 The data at the end of this document measure vectors tangent to a sphere, rounded. Select any closed curve with a positive arc length on the surface of the sphere. Estimate the circulation of the vector field around your curve. Estimate the net outward flow of the vector field around your curve. Optionally, the original data are available at [1, Source Data Fig. 2). zonal velocity -60. -50. . -40. -30. - 20. -10. 0. 10. 20. 30. 40. . 50. 60. 23. 3.5 3.2 3. 3 3.2 3.6 2.4 2.7 2.1 2.9 3.6 3.5 1.9 -3.4 22 4.4 3.8 4. 4.2 3.3 1.7 1.9 2.5 3.1 5. 6.6 7.6 3.4 21. . 3.9 3.5 3.4 3.8 2.9 1.4 1.4 2.4 2.8 4.3 5.5 6.7 3. 20. 0.7 1.9 2.4 2.1 0.8 0.3 1. 2.4 4.4 5.2 4.9 4.5 3.4 19. . 1.2 1.3 1.2 -0.2 -0.8 0. 0.9 2.2 3.3 3.2 2.6 0.8 2. 18. 0.4 0. . -0.3 -1.7 -2.8 -1.5 -0.1 1.8 2.8 1.7 1.7 -0.9 1.1 17. 0.4 -0.7 -1. -2.4 -3.4 -2.6 -1.7 -0.3 -0.2 -1.3 -0.3 -0.4 -0.3 16. -1.6 -1.9 -1.8 -3.4 -4.1 -4.4 -2.6 -2 -0.8 -1.4 0. 0 0.1 -2.2 15. -3. -3.5 -2.5 -2.5 -2.6 -3.3 -2.7 14. -2. -1.9 -1. -0.5 -0.3 -1.1 -0.6 -1. -0.8 -1.6 - 1.6 -1.5 0.2 13 -1.6 -0.8 0.1 1.8 1.2 1.3 1. 2.1 0.2 -0.8 -2.2 -1.1 0.1 12. -0.7 1.4 2.1 2.6 1.6 1.9 2. 3.6 3.1 2.4 0.3 0.6 0.3 11. -0.8 1. 1.1 1.8 1.3 2.9 2.5 3.9 2.6 2.7 1.1 1.7 -2. 10. 0.4 0.9 1.2 2.3 2.5 3.2 2. 2.4 2.4 1.5 0.5 1.2 1 1. 9. 0.7 0.7 0.4 1.7 2.1 3.3 2.1 2.1 1.2 -0.1 -0.6 0.1 1.9 8. 0. 0.7 0.6 1.6 1.3 2.1 1.5 1. 0.2 -1. -0.9 -1. 1.5 7. -0.9 -0.2 0.1 0.5 0.3 1. 1.4 -0.1 -1.3 -1.6 -0.3 -0.8 0.1 6. -1.5 -1.3 -0.5 0. 0.3 -0.6 -0.1 -1.2 -2.6 -3.4 -3. -1.4 0.2 . 5. -0.5 -1.6 -2.9 -3.6 -4. -4.5 -2.6 -3.4 -3.9 -5.3 -4.1 -2.3 -1.5 4. -1.7 -2.9 -3.7 -5. -5.2 -5.1 -3.9 -4.4 -4.7 -4.6 -3.3 -3.2 -2. 3. -2.1 -2.8 -3.6 -5.1 - 6.2 -4.8 -4.7 -4.4 -4.6 -2.4 -1. -1.3 -0.6 2. -1.3 -2.6 -2.2 -2.3 0.8 0.6 -2.7 -4.8 -5.2 -2.2 -2.6 -3.4 1.1 1. -0.3 -0.1 -1.1 -0.2 2.7 2.2 -0.8 -2.8 -2.2 -1.3 -3.9 -4.6 -1.6 . 0. 2.4 2. 1. 1.2 4.8 3.6 2.1 -1.2 0.1 0.4 -1.5 -3.3 -4.6 -2.9 -2.9 -2.9 -1.4 -0.3 -1.1 meridional velocity -60. -50. -40. - 30. -20. -10. 0. 10. 20. 30. 40. 50. 60. 23. -1.7 -0.9 -0.3 1.4 3.1 1.4 0.1 -2. -3.2 -4. -5.3 -4.5 -3.7 22. 0.3 1.5 1.8 3.2 3.2 1.2 -0.4 -2.7 -4.4 -5.6 -6.4 -5.9 -5.4 21. 2.2 2.7 2.8 3.4 2.8 0.9 -0.9 -2.8 -4.4 -5.4 -5. -3.9 -2.8 20. 1.7 2. 2.2 2.4 1.4 0. -1.7 -3.7 -5.5 -6.4 -4.3 -2.2 0. 19. 1.5 1.5 1.9 1.2 1.1 -0.6 -1.8 -3.4 -4.6 -4.4 -3. -0.7 0.8 18. 1.6 1.5 2. 1. . 1. -0.3 -1.9 -3.7 -4.4 -3.7 -2.3 -1. 0.4 17. 0.6 0.4 1.7 0.9 0.8 -0.2 -1.4 -1.9 -2.3 -1.5 -0.4 1.3 2.1 16. -0.7 -1.4 0.3 -0.1 0. -0.1 -0.6 -0.6 -1.9 -1.6 -0.4 2.9 4.9 15. -3. -3.5 -1.7 -1.1 -0.6 -0.5 0.1 0.8 0.3 0. 0 1.4 4.6 5.8 14. -3.8 -4.7 -2.9 -1.6 -0.7 -0.9 -0.3 0.1 0.3 1. . 3. 4.9 3.6 13. -5.1 -6.5 -4.8 -3.1 -1.7 -1.4 -0.5 0.7 2.3 3.4 4.8 4.6 2.5 12. -5.1 -6.3 -5.3 -4.3 -2.7 -1.5 -0.1 1.2 2.9 4.3 5.5 5.6 3.7 11. -5.4 -6.9 -6.5 -5.6 -3.6 -1.3 0.5 1.8 3.1 3.7 4.5 5.1 5.9 10. -5.4 -5.8 -5.2 -4.7 -3.5 -1.5 0.1 1.1 2.5 3.2 4.2 3.6 9. -4.3 -4.5 -4. -3.8 -3.3 -1.8 -0.3 0.4 1.4 2.2 3.3 1.8 0.8 8. -3.2 -2.2 -1.6 -1.4 -1.8 -1 -0.6 0. . 0.2 1.4 2.5 0.9 0. . 7. -1.8 -0.5 -0.2 0.1 -0.2 -0.1 -0.4 -0.6 -1.3 -0.2 0.7 0.3 -0.1 6. -1.5 0.6 1.1 2.2 1.6 0.9 -0.6 -1.5 -2.6 -1.3 -0.1 0.3 -1.4 5. -1.1 1.3 1.9 2.6 1.9 0.2 -0.7 -1.3 -1.6 -0.8 0.2 0.6 -1.7 4. -1.6 0.4 1. 2.2 1.5 0.7 0.1 -0.3 -0.7 0.9 2.8 3.5 0.9 3. -2.5 -1.3 -0.3 0.6 1. 0.6 0.7 1.6 1.5 2.3 3. 3.6 2.9 2. -3.5 -2.7 -2.3 -0.7 0 0.3 0.5 1.6 2.1 2.7 3.4 4.1 2.5 1. 1 - 3.5 -2.8 -2.4 -0.9 0.6 0.4 -0.1 0.4 1.1 0.6 1. 1.1 1.8 0. . -3.7 -2.9 -2.3 -0.2 1.1 0.4 -0.5 -1.3 -1.7 -2. -2.2 -1.7 -0.9 2.4 v (23,60) =(-3.4, -3.7)

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