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A study is made of stability properties of perturbations superimposed on an unstably stratified plane parallel flow with variable vertical shear. Two different types of instability which may take place in the flow are found: one is a thermal instability modified by a shear flow, and the other is an inertial instability modified by a thermal stratification. Unstable perturbations of the thermal type are distinguished from those of the inertial type in terms of the Richardson number. The thermal instability is most favorable for development of a three-dimensional longitudinal perturbation whose wavelength in the direction parallel to the basic flow is much longer than that in the direction perpendicular to the basic flow. A preferred perturbation of the inertial instability, however, is of a two-dimensional transverse mode. Amplification of transverse perturbations of thermal origin is reduced by the influence of a shear flow regardless of the presence of variable shear in the basic flow. We conclude that a shear flow in general is responsible for the formation of longitudinal convection roll, and a variable shear slightly affects characteristics of thermal instability of a constant shear flow.

Stability of a Plane Parallel Flow with Variable Vertical Shear and Unstable Stratification