In this thesis I will present two experimental studies of relative diffusion.
The former is a study of relative diffusion on capillary waves. I will refer
to this experiment as the *Faraday wave experiment* or just the
*Faraday experiment*. The latter is a study of relative diffusion in grid
turbulence in a flowing soap film.

The first study of relative motion of pairs of particles in turbulence was
reported by Lewis F. Richardson in 1926 [13].
His argument for studying relative motion, rather than absolute motion, is
that it removes the background flow.
Richardson found in a collection of measurements, ranging in length scales
from to , that the diffusivity, *K*, grows as a power of
the length scale, *l*:

15 years after Richardson's study was published, the Russian statistician
A. N. Kolmogorov made a strong formal definition of turbulence based on the
probability distribution of a velocity field, and used it to derive an
expression for relative diffusion in turbulent velocity fields. Kolmogorov
describes relative diffusion in terms of the averaged relative velocities of
pairs of particles, , as a function of the particle
separation, *R*:

More recent developments of the theoretical framework includes the theory of weak turbulence (see for instance [14]), which can be applied to relative diffusion in the Faraday wave experiment.

The measurements on the Faraday wave experiment, which I present here were made at the Niels Bohr Institute in 1993 and 1994 by Mogens T. Levinsen, Walter I. Goldburg and myself. Analyses of these measurements have previously been reported in [1, 15, 7, 16] (the three first of these papers can also be found as appendices C, D, and E).

The soap film experiment was set up during my visit at Goldburg's laboratory at University of Pittsburgh in 1994 and 1995. The goal with this experiment was to use the processing techniques I developed for the Faraday experiment on a two-dimensional fluid experiment. Due to an unfortunate choice in the design of the experiment, the value of the measurements for the study of two-dimensional fluid dynamics is doubtful.

I have appended an index to the thesis. It is far from complete, but I hope it will make it easier to navigate my thesis anyway.