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The current work deals with the numerical analysis of linear stability problems in astratied plain Poiseuille ow of air over water with equal layer heights. The interaction and branch exchange between Tollmien–Schlichting instability in air and interfacial instability is discovered and investigated. This effect is shown to stabilize disturbances with wavelengths of the order of channel height for interfacial waves and to produce a closed stable region inside the neutral curve of the interfacial mode. The behaviour of three unstable modes in the problem, corresponding to Tollmien–Schlichting type instability in air and water layers and interfacial instability respectively, has been studied in detail.Neutral conditions for all three modes and the stable region have been calculated

On the patterns of interaction between shear and interfacial modes in plane air–water Poiseuille flow