Asymptotic Study of Instability in a Three-Layer Stokes Flow with an Inhomogeneous Layer Thickness. Modeling of the Folding Process

Abstract

Zero-Reynolds-number instability in a three-layer Stokes flow of viscous fluid with an inhomogeneous layer thickness in a two-dimensional region with a free boundary is investigated. The method of multiple scales is applied for constructing an asymptotic expansion of the solution of the boundary-value problem for the Stokes equations. The stability of the system of first-approximation equations is analyzed using the Fourier method, and it is concluded that the most significant increase in the zero-Reynolds-number instability occurs in a region of waves whose lengths are comparable with the thickness of the middle layer. In contrast to the case of a constant layer thickness, the instability parameters are variables. The mechanism of formation of geological folds is studied.