The paper discusses possibilities for refinements of conventional ''eq
uilibrium'' second-moment turbulence closure models, aimed at improvin
g model performances in predicting turbulent flows of greater complexi
ty. In focus are the invariant modelling of the low-Re-number and wall
proximity effects, as well as extra strain-rates and control of the t
urbulence length-scale. In addition to satisfying most of the basic ph
ysical constraints, the main criterion for model validation was the qu
ality of reproduction of flow and turbulence details, particularly, in
the vicinity of a solid wall, in a broad variety of non-equilibrium f
lows featured by different phenomena. It is demonstrated that the new
model, which includes several new modifications, but also some propose
d in the past, can satisfactorily reproduce a range of attached and se
parating flows with strong time- or space-variations or abrupt changes
of boundary conditions. Cases considered cover a wide range of Re-num
bers involving in some cases also the laminar-to-turbulent or reverse
transition.