Kelvin–Helmholtz instability in a Hele-Shaw cell: Large effect from the small region near the meniscus

Abstract

In an attempt to improve the poor prediction of our previous theory, we examine corrections from the small region in a Hele-Shaw cell near the meniscus where the flow is three dimensional. At larger Reynolds numbers, we find an O(1) change to the effective boundary condition for mass conservation which is to be applied to the large scale flow outside the small region.