Non-parallel shear flows of an inviscid, incompressible, density-stratified fluid are considered. The stability is studied in terms of the possibility of complete mixing within a horizontal layer of given thickness. It is assumed that the energy interchange between the mixed region and the external fluid can be neglected. It is also assumed that the required turbulent energy is greater than the energy needed to invert the region to be mixed. The term ‘stable’ as used here means that the kinetic energy released by making the velocity constant over the layer thickness is not sufficient to provide the required turbulent energy for that layer thickness.

If each horizontal fluid plane has a translational velocity of the same magnitude and shear is produced by rotation of the velocity vector with increasing height, then ‘stability’ increases strongly with increasing layer thickness.