Asymptotic study of instability in a three-layer Stokes flow with an inhomogeneous layer thickness. Folding process simulation

Instability at zero Reynolds numbers in a three-layer Stokes flow of a viscous fluid with an inhomogeneous layer thickness in a two-dimensional region with a free boundary is investigated. The method of multiple scales to 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 instability at zero Reynolds numbers occurs in the 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 variable. The mechanism of formation of geological folds is investigated.