How can I model ink dropped into still water? I want to be able to model an opaque liquid being dropped into a transparent liquid with sufficient velocity to cause turbulence and the resulting chaotic mixing. Assuming the two liquids are of the same density and viscosity, how could I model this?

This doesn't need to be rendered in real time. I would like the turbulent flow to gradually settle down as the two fluids mix, but it will not be required to interact with other objects.

I've tried modelling an expanding interface between the two fluids, and accelerating the vertices of the interface based on the local curvature, adding new vertices as they move apart. This seemed to work in the early stages, giving a constant exaggeration of small surface imperfections to create at least the appearance of turbulence, but it ran into problems very early which seemed to result from the interface self-intersecting. I've been trying to think of ways to redirect vertices that are near to causing a surface self-intersection, but I wonder if I would be better off starting from scratch with a more amenable method.
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.