Harmonic moment dynamics in Laplacian growth.

Harmonic moments are integrals of integer powers of z=x+iy over a domain. Here, the domain is an exterior of a bubble of air growing in an oil layer between two horizontal closely spaced plates. Harmonic moments are a natural basis for such Laplacian growth phenomena because, unlike other representations, these moments linearize the zero surface tension problem [S.

Fjords in viscous fingering: selection of width and opening angle.

Our experiments on viscous fingering of air into oil contained between closely spaced plates reveal two selection rules for the fjords of oil that separate fingers of air. (Fjords are the building blocks of solutions of the zero-surface-tension Laplacian growth equation.) Experiments in rectangular and circular geometries yield fjords with base widths lambda(c)/2, where lambda(c) is the most unstable wavelength from a linear stability analysis.