Weakly nonlinear investigation of the Saffman-Taylor problem in a rectangular Hele-Shaw cell
arXiv:cond-mat/9711270 · doi:10.1142/S0217979298000521
Abstract
We analyze the Saffman-Taylor viscous fingering problem in rectangular geometry. We investigate the onset of nonlinear effects and the basic symmetries of the mode coupling equations, highlighting the link between interface asymmetry and viscosity contrast. Symmetry breaking occurs through enhanced growth of sub-harmonic perturbations. Our results explain the absence of finger tip-splitting in the early flow stages, and saturation of growth rates compared with the predictions of linear stability.
42 pages, 5 figures, added references, minor changes, to appear in Int. J. Mod. Phys. B (1998)