Multiscale analysis of non-equilibrium boundary layers at moderate Reynolds numbers

Turbulent boundary layers with mean-flow three dimensionality occur frequently in complex flow configurations. In these cases, the mean flow direction changes continuously across the boundary layer thickness due to the cross-stream pressure gradient induced by the geometry of the immersed body. This results in counter intuitive reduction of turbulent stresses, with important implications for turbulence modeling. We investigate temporally developing three
dimensional turbulent boundary layers at friction Reynolds numbers up to 1000 using direct numerical simulation of planar channels subjected to a sudden spanwise pressure gradient. It is shown that the scaling properties and regimes of the flow across different Reynolds numbers can be explained in terms of a hierarchy of self-similar wall-attached eddies with characteristic time-scales proportional to their distance the wall. These momentum-carrying eddies are shown to undergo Reynolds stress depletion caused by the formation of a spanwise boundary layer which inhibits the redistribution of energy via pressure-strain correlation. Our findings answer fundamental questions regarding the structural changes of equilibrium wall-turbulence under the imposition of additional strain.