Near wall region behavior of unsteady layers with favorable and adverse pressure gradients

A one equation turbulence model is used together with an implicit numerical scheme to investigate the behavior of unsteady turbulent boundary layers. Free stream velocity distributions with zero, adverse, and favorable pressure gradient in mean have been considered. The numerical results obtained at different frequencies have been compared with the available experimental data. At high frequencies good comparisons for the phase have been obtained between numerical and experimental data, while at low frequencies there is not agreement. A theoretical analysis has been done which explains the numerical results, in the region very close to the wall. The behavior of turbulent quantities has been analyzed but due to the lack of experimental data in the near wall region a quantitative comparison can not be done. From the qualitative point of view the numerical simulation is able to predict the experimentally evidenced high turbulence levels in the viscous regions, and Reynolds stress freezing in the log region.