A number of qualitative properties of a first-order gradient transport model for turbulent density-stratified flow is analyzed. The dynamical stability of a statically stable shear flow is considered to re-examine certain arguments found in the literature which are in favour of the possibility of instability. Real flows seem to be stable in the sense that in homogeneous turbulence sharp interfaces do not arise spontaneously. Furthermore the development of an interface between two homogeneous layers is dealt with, and is found to be in line with the stability analysis and with experimental evidence reported in the literature.