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.

中文翻译：

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具有非均匀层厚度的三层斯托克斯流中的不稳定性的渐近研究。折叠过程建模

研究了具有自由边界的二维区域中层厚不均匀的粘性流体的三层斯托克斯流中的零雷诺数不稳定性。应用多尺度方法构造斯托克斯方程边值问题解的渐近展开式。使用傅立叶方法分析了一次近似方程组的稳定性，得出的结论是，零雷诺数不稳定性的最显着增加发生在长度与中间厚度相当的波区域中。层。与恒定层厚度的情况相反，不稳定参数是可变的。研究了地质褶皱的形成机制。