| Description: |
This paper reports on a study of the contribution of the velocity-vorticity correlations to the skin friction in incompressible turbulent boundary layer (TBL) flows and their variation with the pressure gradient. Direct numerical simulations (DNSs) are performed for three TBL cases with different pressure gradients, namely a zero pressure gradient (ZPG), a mild adverse 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 nondimensional pressure 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-field streamwise pressure gradient. The contribution of the velocity-vorticity correlations to the skin 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 negligible when compared to the other components and does not change with the pressure gradient. The contribution from the molecular diffusion at the wall (Cf3) increases with the pressure gradient and becomes a dominant contributor in reducing the skin friction coefficient when the flow reaches the verge of separation. For the strong APG TBL, the primary contribution to the outer 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!0z i. is the boundary layer thickness. For all the pressure gradient cases, the contribution of the 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 the combined contribution of the advective vorticity transport and the vortex stretching terms can be considered as the contribution from the Reynolds shear stress with a constant weight (Cf12c) for all the pressure ... |