Animation of Arbitrary Surface Oscillations of a Water Droplet

Oscillations on the surface of a water droplet. No damping effects are modeled and all modes are pure harmonics with arbitrary radial oscillation amplitudes.

Modes are based on spherical harmonics. Mode frequencies are derived under the assumptions:
* For small amplitude oscillations surface tension is the dominant restoring force.
* Water is an incompressible fluid (no breathing mode).
* Curvature of the surface remains continuous (surface tension is never overcome).

The details of the mode frequencies are drawn out in Lamb's "Hydrodynamics". This was my final project for the Theoretical Mechanics II course at Michigan Technological University in the Physics Department. If anyone is particularly interested I can upload a copy of my final report which covers in detail the derivations from Lamb as well as the programmatic design of the animation.

It is interesting to note that most of the theory applied here came from books on Seismological oscillations. With a few modifications and differences the model here could model earthquakes; although one would certainly have to re-examine the derivation of the modes and mode frequencies as assumptions are invalidated for this regime. For example, oscillations of a droplet are purely radial. An earthquake model would have to include rotational and shearing motions as well.

Modeled in MATLAB.

Видео Animation of Arbitrary Surface Oscillations of a Water Droplet канала Daniel Miller