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

<p dir="ltr">This paper reports on a study of the contribution of the velocity-vorticity correlations to</p><p dir="ltr">the skin friction in incompressible turbulent boundary layer (TBL) flows and their variation</p><p dir="ltr">with the pressure gradient. Direct numerical simulations (DNSs) are performed for three</p><p dir="ltr">TBL cases with different pressure gradients, namely a zero pressure gradient (ZPG), a mild</p><p dir="ltr">adverse pressure gradient (mild APG), and a strong adverse pressure gradient (strong APG)</p><p dir="ltr">TBLs. The strong APG TBL, which is at the verge of separation, has an average nondimensional</p><p dir="ltr">pressure gradient () value of 39 within the domain of interest. = 1Pe;x=w,</p><p dir="ltr">where 1 is the displacement thickness, w is the mean wall shear stress and Pe;x is the far-field</p><p dir="ltr">streamwise pressure gradient. The contribution of the velocity-vorticity correlations to the</p><p dir="ltr">skin friction coefficient are computed based on the decomposition presented by Yoon et al.</p><p dir="ltr">(2016). The contribution of the molecular transfer due to the mean vorticity (Cf4) is negligible</p><p dir="ltr">when compared to the other components and does not change with the pressure gradient. The</p><p dir="ltr">contribution from the molecular diffusion at the wall (Cf3) increases with the pressure gradient</p><p dir="ltr">and becomes a dominant contributor in reducing the skin friction coefficient when the flow</p><p dir="ltr">reaches the verge of separation. For the strong APG TBL, the primary contribution to the</p><p dir="ltr">outer peak of the negative wall-normal gradient of the Reynolds shear stress (��@hu0v0i=@y),</p><p dir="ltr">located around the height of y= = 0:3, is from the velocity-vorticity correlation hv0!0z</p><p dir="ltr">i.</p><p dir="ltr">is the boundary layer thickness. For all the pressure gradient cases, the contribution of</p><p dir="ltr">the advective vorticity transport term (Cf1) is negative, whereas the vortex stretching term</p><p dir="ltr">(Cf2) provides a positive contribution to the skin friction coefficient. It is shown that the</p><p dir="ltr">combined contribution of the advective vorticity transport and the vortex stretching terms</p><p dir="ltr">can be considered as the contribution from the Reynolds shear stress with a constant weight</p><p dir="ltr">(Cf12c) for all the pressure gradient cases. When the flow reaches the verge of separation in the</p><p dir="ltr">strong APG TBL, the vortical motions and turbulent mixing in the outer layer become more</p><p dir="ltr">important in relation to the contribution of the Reynolds shear stress and its wall-normal</p><p dir="ltr">gradient (@hu0v0i=@y) to the skin friction. An alternate method, based on the RD identity</p><p dir="ltr">(Renard and Deck, 2016), to compute the contribution of the velocity-vorticity correlations</p><p dir="ltr">is also discussed.</p>