Instability of Time-Periodic Flows of Stratified Fluids

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Abstract
The instability of two liquid layers with a free surface set in motion by an oscillatory lower boundary is analyzed for two superposed fluids with different viscosities and different densities. There are two modes of wave motion: the interfacial and the free‐surface modes. When the Froude number is less than about 3, the interfacial mode governs the instability of the flow. For this case the free‐surface mode is always stable. The two surfaces of discontinuity are always in the phase for the free‐surface mode of disturbance, but may be in phase or 180 deg out of phase for the interfacial mode. The two modes, however, are found to compete with each other for governing the instability of the flow when the Froude number is larger than 3. The two surfaces of discontinuity can be out of phase by an angle different from 180 deg