 Vortex-induced force on a plane wall

A vortex of circulation $\Gamma$ distance $d$ from a plane wall has an opposite-sign image across the wall. The wall velocity has magnitude $|\Gamma |d/[\pi (d^2+y^2)]$, giving a pressure reduction $\rho {\Gamma }^2{d}^2/[2{\pi }^2(d^2+y^2{)}^2]$ by the Bernoulli equation. Integrating this deficit gives the displayed force per unit width, directed from the wall toward the fluid and vortex. The uniform ambient pressure is subtracted to isolate the finite vortex-induced force.