How can I model ink dropped into still water?
Simulating drops of ink is probably one of the best applications of the Vorton Method.

Unlike fluid solvers based on the velocity form of the Navier-Stokes equations, which track the density and velocity of a fluid, the Vorton Method tracks vorticity instead. It does so by simulating a large number of vortons, each carrying a small amount of vorticity; you can think of a vorton as being a tiny particle that induces a small spinning vortex around itself. The sum of velocities caused by each vortex defines a velocity field in the fluid, which is used to in turn advect the vortons themselves.

Vorton methods are difficult to combine with boundary conditions and have a few efficiency caveats, but for fluid flow where intricate turbulance is the key feature and boundaries can be avoided, the Vorton method far outshines e.g. Eulerian grid solvers, which would need a large resolution to simulate turbulence at a comparable scale.

Michael Gourlay has a very accessible article series on the vorton method. Although his articles are targeted at video games, they hold up similarly for off-line simulation. Here's also an example video of a drop of ink simulated using the vorton method.