Analysis of the factors contributing to the skin friction coefficient in adverse pressure gradient turbulent boundary layers and their variation with the pressure gradient

This paper reports on a study of the contribution of the velocity-vorticity correlations tothe skin friction in incompressible turbulent boundary layer (TBL) flows and their variationwith the pressure gradient. Direct numerical simulations (DNSs) are performed for threeTBL cases with different pressure gradients, namely a zero pressure gradient (ZPG), a mildadverse pressure gradient (mild APG), and a strong adverse pressure gradient (strong APG)TBLs. The strong APG TBL, which is at the verge of separation, has an average nondimensionalpressure gradient () value of 39 within the domain of interest. = 1Pe;x=w,where 1 is the displacement thickness, w is the mean wall shear stress and Pe;x is the far-fieldstreamwise pressure gradient. The contribution of the velocity-vorticity correlations to theskin friction coefficient are computed based on the decomposition presented by Yoon et al.(2016). The contribution of the molecular transfer due to the mean vorticity (Cf4) is negligiblewhen compared to the other components and does not change with the pressure gradient. Thecontribution from the molecular diffusion at the wall (Cf3) increases with the pressure gradientand becomes a dominant contributor in reducing the skin friction coefficient when the flowreaches the verge of separation. For the strong APG TBL, the primary contribution to theouter peak of the negative wall-normal gradient of the Reynolds shear stress (􀀀@hu0v0i=@y),located around the height of y= = 0:3, is from the velocity-vorticity correlation hv0!0zi.is the boundary layer thickness. For all the pressure gradient cases, the contribution ofthe advective vorticity transport term (Cf1) is negative, whereas the vortex stretching term(Cf2) provides a positive contribution to the skin friction coefficient. It is shown that thecombined contribution of the advective vorticity transport and the vortex stretching termscan be considered as the contribution from the Reynolds shear stress with a constant weight(Cf12c) for all the pressure gradient cases. When the flow reaches the verge of separation in thestrong APG TBL, the vortical motions and turbulent mixing in the outer layer become moreimportant in relation to the contribution of the Reynolds shear stress and its wall-normalgradient (@hu0v0i=@y) to the skin friction. An alternate method, based on the RD identity(Renard and Deck, 2016), to compute the contribution of the velocity-vorticity correlationsis also discussed.