Transition of a temporally developing three-dimensional turbulent boundary layer

A temporally developing three-dimensional turbulent boundary layer is investigated using direct numerical simulation. The flow is initiated by subjecting a statistically stationary turbulent channel flow to a constant transverse pressure gradient while maintaining the streamwise pressure gradient unchanged. It is shown that this nonequilibrium three-dimensional boundary layer can be described as a turbulent-turbulent transition that is characterized by the development of a laminar boundary layer in an initial turbulent environment followed by a transition to turbulence. Both transient energy growth and crossflow instability may influence the transition, though the former is likely to have a stronger effect when the initial Reynolds number is lower and the transverse pressure gradient is stronger. The transient developments of both the mean flow and turbulence are understood by relating them to the process of transition. The rotation of streaks and the damping effect of the spanwise boundary layer work together to suppress the streamwise and wall-normal turbulence. This effect is stronger than the energy growth in the spanwise direction, causing the overall turbulent kinetic energy and the structure parameter to decrease, explaining the observations made of such flows.