Abstract
The direct Lyapunov method is used to prove the absolute linear instability of steadystate plane-parallel shear flows of an inviscid stratified incompressible fluid in the gravity field with respect to plane perturbations both in the Boussinesq and non-Boussinesq approximations. A strict description is given for the applicability of the known necessary condition for linear instability of steady-state plane-parallel shear flows of an ideal nonuniform (by density) incompressible fluid in the gravity field both in the Boussinesq and non-Boussinesq approximations (the Miles theorem). Analytical examples of illustrative character are constructed.
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