In many stratified environmental flows, the effects of gravity on density profiles have a dual role. On one hand, density differences drive flow downstream, and on the other hand, they influence the turbulence field itself, modifying transport capacity. This effect is clearly seen, for example, in turbidity currents, where the flow is driven by suspended sediment displaying a non-uniform vertical profile. On top of this, flows take place in complex geometries, inducing secondary flows with an important impact, for instance, on bed scouring. The integral analysis of this flow setup is a difficult task that needs to be done systematically. This study aims to isolate and separately analyze the effect of the non-uniform driving force on secondary motions generated in a turbulent flow in a straight duct of square section. To achieve this, stratified forcing is modeled as a non-uniform force in the vertical direction. Fully resolved direct numeric simulations are performed using a pseudo-spectral code that implements Fourier expansions in the flow direction and Chebyshev expansions in the other two directions. Simulation results reveal a loss of symmetry on the vertical for the mean flow and a shift of the main velocity maximum toward the bottom wall. Secondary flow upper vortices extend into the bottom half of the duct, modifying vortex patterns and consequently impacting the distribution of wall shear stress. Additionally, variations in velocity root mean square values are observed, indicating turbulence modulation in the bottom half section.
Martorana et al. (Mon,) studied this question.