Fluids on Surface

  1. Flow converges to a steady state corresponding to a Killing vector field, from initial velocity profile: $u = (10\cos(2x)\sin(2y),\, 10\sin(xy))$ and $u = (\sin x\cos y,\, \cos(xy))$, respectively. sphereb spherkilling
  2. Flow on a helicoid converging to the steady state from initial velocity: $\left(\sin(\pi x)\cos(\pi y), -\cos(\pi x)\sin(\pi y)\right)$. helicoid
  3. The first ten eigenvector fileds of the modified Hodge Laplacian $(\Delta u)^k = g^{ij}u^k_{;ij} + R^k_ju^j$ on a sphere and torus. worm worm
  4. Surface flow around a cylinder. flowcylinder