- Dynamics Of Deformable Media 1 (29.83 KiB) Viewed 9 times
DYNAMICS OF DEFORMABLE MEDIA
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DYNAMICS OF DEFORMABLE MEDIA
DYNAMICS OF DEFORMABLE MEDIA
There are two right vortices, whose nucleus has radius a. Inside the nucleus the vorticity is constant, being its magnitude w and outside the nucleus the vorticity is zero. The direction of the vorticity vector is parallel to the axis of symmetry of the straight tube. a) Find the velocity field for r < a and r > a. b) Consider two vortices such that one has positive vorticity and the other has negative vorticity (the magnitude of the vorticity is the same). Show that in this case the vortices move with constant speed and equal to: г U 2πd where d is the distance between the centers of the vortices and I is the circulation. This result is valid provided that d > a. What happens if d < a? Explain. c) Consider now that the two vortices are of the same sign. Show that in this case the vortices rotate around a common center and find the angular speeld of rotation.
There are two right vortices, whose nucleus has radius a. Inside the nucleus the vorticity is constant, being its magnitude w and outside the nucleus the vorticity is zero. The direction of the vorticity vector is parallel to the axis of symmetry of the straight tube. a) Find the velocity field for r < a and r > a. b) Consider two vortices such that one has positive vorticity and the other has negative vorticity (the magnitude of the vorticity is the same). Show that in this case the vortices move with constant speed and equal to: г U 2πd where d is the distance between the centers of the vortices and I is the circulation. This result is valid provided that d > a. What happens if d < a? Explain. c) Consider now that the two vortices are of the same sign. Show that in this case the vortices rotate around a common center and find the angular speeld of rotation.