There are still many interesting measurements that have to be made on Faraday waves.
Both the temporal and spatial resolution in the measurements of relative diffusion could be increased by a factor 100 by recording successive positions of collections of particles on colour film using different colours of illumination for each time step.
It is of great importance to know the energy dispersion in the experiment, when you want to relate measurements to present turbulence theory. We have until now only tried to measure it by looking at the power we put into the vibration exciter. Using a lighter vibration exciter would probably yield better results. Another option is to measure the decay of the wave amplitude immediately after the external forcing has stopped, and use that to calculate the energy dissipation. If we let m denote the mass of the fluid, let denote the amplitude of the waves, and let denote the frequency of the waves, a rough estimate gives us that the energy is , and the energy dissipation is thus .
The quality of measurements of fractional Brownian motion (see appendix E) could probably be improved a lot by recording single particle tracks on photographic film, and then calculating the fractal dimension from the picture.
It would be nice somebody could explain why relates to R as it does, and what meaning it has.
The processing of images of particle traces needs to be changed, so it can distinguish an image of two overlapping particle traces from the trace of a single particle. Checking if there is more than one concave section on the outline of the trace might do the job.
I am grateful for all the help I got while I worked on the experiments and while I wrote this thesis. Many people have helped me through this process with discussions, encouragement, suggestions and solutions.
And the spirit can not live without the body so: Thanks to SU-styrelsen, Lørup-fonden (and Tofta Teld :-) for funding my studies.