The problem of potential flow past a circular object is a well-studied problem in fluid mechanics governed by the Laplace equation. We wish to study the flow around a circle which is slightly perturbed. The boundary is now described as \[r=R(1+\epsilon \cos \theta)\]
The solution for the streamfunction for the base problem where the boundary is at \(r=R\) is that for a circle studied. Now set up the domain perturbation analysis for this problem with the above perturbed boundary and solve for the modified domain.