The nonlinear growth of a gravitationally unstable interface in a Hele-Shaw cell

Abstract

We report observations of the nonlinear growth of an unstable interface in, a large Hele-Shaw cell in which it is possible, in the most extreme case, to follow the emergence of a single ‘finger’ from approximately thirty initial wavelets. The larger ‘fingers’ that emerge undergo further instability to form a highly contorted interface. We have measured a number of the averaged characteristics of this interface and can relate the various cases studied through length and time scales constructed from the independent parameters of the problem. We show that the most distorted interfaces may have a fractal dimension at scales larger than the instability wavelength and discuss the significance of this possibility.