In this paper, some recent developments of two turbulence closure sche
mes at ICOMP, NASA Lewis will be discussed. One is the Reynolds-stress
algebraic equation model and the other is the Reynolds-stress transpo
rt equation model. Various model constraints required by the rapid dis
tortion theory, the invariant theory and the realizability principle,
etc. will be described in the model development. The models discussed
are for high-turbulent Reynolds number flows, so that the near-wall tu
rbulence and the low-Reynolds-number turbulence are not discussed here
.