A tornado in the shape of a cylinder with a diameter of 100 m has an axis of rotation through its center which is along the vertical direction. The sense of rotation is cyclonic (counterclockwise). The wind is purely rotational, with a wind speed given by V=0.8r m/s, where r is the distance from the axis.
a. Find the circulation C at r=100m
b. Find the curvature and shear contributions to the vorticity (eta) as well as eta itself.
c. Due to vertical stretching, the radius of the tornado decreases to 50 m. What is the final vorticity, assuming that it remains uniform.