Boundary-Layer Separation: Thwaites & von Kármán Vortex Street (2D)

This 2D companion to the 3D wind-tunnel model swaps the rendered scene for a real numerical solver: Thwaites' momentum-integral method and Michel's transition criterion compute where the laminar boundary layer actually separates from a circular cylinder in potential flow, and Head's entrainment method with the Ludwieg–Tillmann skin-friction law computes where a tripped or naturally-transitioned turbulent layer separates instead — reproducing the classic drag-crisis jump in separation angle from first principles rather than an interpolation table. The resulting separation points feed a genuine discrete-vortex wake: alternating point vortices are shed at the Strouhal frequency, each one advected by every other vortex plus its own image inside the cylinder (method of images) plus the free stream, so the von Kármán street you see rolling up downstream is computed vortex dynamics, not a scripted animation.