Homogeneous Differential Equations

We simulate the advection of a passive scalar by a simple rotation flow u, generating a converging spiral. In particular, we use a simple flow with |u|~r², such that angular velocity increases linearly with the distance to the center. The solution is exact, calculated by differential rotation of the initial condition by |u(r)|/r for each radius r. Rotation speed is chosen such that a complete outer rotation is achieved at t=1. #physics #mathematics #differentialequations #calculus #visualization