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Updated: May 9, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Instability modes of a two-layer Newtonian plane Couette flow past a porous medium
A Ananth Praveen Kumar1, Himanshu Goyal, Tamal Banerjee
1Department of Chemical Engineering, Indian Institute of Technology, Guwahati, India.
Abstract:
We explore the salient features of the different instability modes of a pressure-driven two-layer plane Couette flow confined between a moving wall and a Darcy-Brinkman porous layer. A linear stability analysis of the conservation laws leads to an Orr-Sommerfeld system, which is solved numerically with appropriate boundary conditions to identify the time and length scales of the instability modes. The study reveals that the movement of the confining wall together with the slippage at the porous-liquid interface originating from the flow inside the porous layer can stimulate a pair of finite-wave-number shear modes in addition to the long-wave interfacial mode of instability. The shear modes dominate the interfacial mode, especially when the frictional influence at the liquid layers is smaller due to the movement of the confining plate or due to the larger slippage at the porous-liquid interface. The shear modes are found to be present under all combinations of the viscosity μ(r) and thickness h(r) ratios of the liquid layers. This is in stark contrast to the two-layer flow confined between nonporous plates where the interfacial (shear) mode is observed only when μ(r)>h(r)(2) (μ(r)
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