 Solution

ID: past-exam-of-the-fluids-and-waves-course-of-the-university-of-oxford/2021/2/b/i/solution

The line vortex is mapped to

ζ_{0} = g (c) = c + \frac{1}{c} .

Its imaginary part is positive because

c

lies in the fluid region. A conformal map preserves the circulation of the local line vortex, so its strength in the mapped complex plane is still

Γ

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