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A study is made of a family of steady two-dimensional Stokes flows stirred by an infinitesimal rotating cylinder (a line rotlet) inside a corrugated boundary. Parameters govern the position of the stirrer and the number and sharpness of ridges in the boundary. A solution is found in terms of a finite combination of elementary functions. It is demonstrated that the flow exhibits some interesting dynamical features such as peculiar bifurcations and homoclinic orbits.doi:10.1090/qam/1218372 fatcat:srfkb5hrvvhbpcl66qvvlznn6q