This report presents a study on the behaviour of particle clouds in two-dimensional velocity fields. The results can be applied in a general way but are especially of interest for the dispersion of matter in surface waters of a large horizontal extent and relatively small depth or layer thickness. They may be somewhat more relevant to seas than to lakes, because at sea the energy supply feeding the velocity field contains an important constant component (of astronomical origin) so that the energy content (at various length scales) of the velocity field will not fluctuate as strongly as may be the case in lakes. Synthetic fields have been used of well defined spectral structure so that numerical experiments could be performed under controlled conditions, which is not possible in nature. By comparing the results with experiments and observations in the field, one obtains insight into natural conditions and prevailing mechanisms and how to model these adequately. Present computer facilities do not only enable these basic studies with synthetic fields of detailed spectral structure but also make it possible to supplement existing flow models with spectral modes which are not reproduced by the flow model while they are essential for proper modelling of dispersion. Sometimes simpler means to the same end with less computational effort are permissible although they remain inferior to the spectral approach.