Non-parallel-flow stability of a two-dimensional buoyant plume

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Abstract
The linear stability of a two-dimensional buoyant plume is analysed by taking into account the transverse velocity component and the streamwise variations of the basic flow and of the disturbance waves. The solutions indicate the dependence of the spatial amplification rate and wavenumber on the disturbance flow quantity under consideration as well as on the streamwise and transverse coordinates. The use of the flow quantity relative to the basic flow leads to close agreement with the neutral curve according to quasi-parallel-stability theory, the usual method for treating nearly parallel flows. However, the amplification rate within an unstable region shows substantial deviation from that predicted by the quasi-parallel theory. The validity of this non-parallel theory is supported by the existing experimental data.

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