  Flow over a surface can be stratified by imposing a fixed mean vertical
temperature (density) gradient profile throughout or via cooling at the
surface. These two distinct mechanisms can act simultaneously as well to
establish a stable stratification in a flow. Here, we perform a series of
direct numerical simulations of open channel flows to study adaptation of a
neutrally stratified turbulent flow under the combined or independent action of
the aforementioned stratification mechanisms. When both stratification
mechanisms are active, the dimensionless stratification perturbation number
enters the picture as an external flow control parameter, in addition to the
Reynolds, Froude, and Prandtl numbers. Additionally, we force the fully
developed flow with constant mass flow rate. This alternative way of forcing
the flow enables us to keep the bulk Reynolds number constant throughout our
investigation and avoid complications arising from the acceleration of the bulk
flow when a constant pressure gradient approach to drive the flow were to be
adopted instead. We demonstrate that significant deviations from the original
Monin-Obukhov similarity formulation are possible when both stratification
mechanisms are active within an otherwise weakly stable flow with contiguous
turbulence, even when the flux Richardson number is well below 0.2.Independent
of active stratification mechanisms, the degree of deviation from neutral
dimensionless shear as a function of the vertical coordinate emerges as a good
measure for the strength of stable stratification for the six different cases
investigated in this study. An extended version of the Monin-Obukhov similarity
also shows promise.
