Whirlpool Drain Vortex: Rankine Model & Free-Surface Dip (2D)

This 2D companion replaces the decorative 3D funnel mesh with the actual mechanics that shape a draining whirlpool: a Rankine combined vortex sets the tangential flow field (solid-body core matched to a free-vortex tail), cyclostrophic balance turns that into a real free-surface height profile you can read off a live cross-section graph, and Torricelli's law through the adjustable drain opening drives a mass-conserving radial inflow that pulls the tracer particles into genuine inward spirals rather than a scripted animation. Four sliders — circulation, core radius, drain radius and viscous decay rate — each change a distinct term in the underlying equations, and the live readout panel reports circulation, core tangential speed, center surface dip and drain outflow rate as they respond.