Two-finger selection theory in the Saffman-Taylor problem.
We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two unequal fingers advancing with the same velocity but with different relative widths lambda1 and lambda2 and different tip positions. For vanishingly small dimensionless surface tension d0, an infinite discrete set of values of the total filling fraction lambda=lambda1+lambda2 and of the relative individual finger width p=lambda1/lambda are selected out of a two-parameter continuous degeneracy. They scale as lambda-1/2 approximately d0(2/3) and p-1/2 approximately d0(1/3). The selected values of lambda differ from those of the single finger case. Explicit approximate expressions for both spectra are given.
Magdaleno
F X
FX
Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Avenida Diagonal, 647, E-08028-Barcelona, Spain.
Casademunt
J
J