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The turbulent boundary layer over a Gaussian shaped bump is computed bydirect numerical simulation (DNS) of the incompressible Navier-Stokesequations. The two-dimensional bump causes a series of strong pressuregradients alternating in rapid succession. At the inflow, the momentumthickness Reynolds number is approximately 1,000 and the boundary layerthickness is 1/8 of the bump height. DNS results show that the strong favorablepressure gradient (FPG) causes the boundary layer to enter a relaminarizationprocess. The near-wall turbulence is significantly weakened and becomesintermittent, however relaminarization does not complete. The streamwisevelocity profiles deviate above the standard logarithmic law and the Reynoldsshear stress is reduced. The strong acceleration also suppresses the wall-shearnormalized turbulent kinetic energy production rate. At the bump peak, wherethe FPG switches to an adverse gradient (APG), the near-wall turbulence issuddenly enhanced through a partial retransition process. This results in a newhighly energized internal layer which is more resilient to the strong APG andonly produces incipient flow separation on the downstream side. In the strongFPG and APG regions, the inner and outer layers become largely independent ofeach other. The near-wall region responds to the pressure gradients anddetermines the skin friction. The outer layer behaves similarly to a free-shearlayer subject to pressure gradients and mean streamline curvature effects.Results from a RANS simulation of the bump are also discussed and clearly showthe lack of predictive capacity of the near-wall pressure gradient effects onthe mean flow.

Direct Numerical Simulation of a Turbulent Boundary Layer with Strong Pressure Gradients