Analysis of the flow in layered fluids at small, but finite, amplitude with application to mullion structures

An analysis of the flow in layered viscous fluids at small, but finite amplitude is illustrated in an application to the shortening of two different viscous fluids parallel to their interface. The analysis extends the familiar infinitesimal amplitude analysis, which retains terms to first-order in the surface slope, to second-order in this quantity. To second-order accuracy, the asymmetry in interface form characteristic of the finite-amplitude lobe-and-cusp structure emerges. Additional results for mullion structures are derived and used to interpret some natural structures.