Contribution of large-scale motions to the skin friction in a moderate adverse pressure gradient turbulent boundary layer

Direct numerical simulation of a turbulent boundary layer (TBL) subjected to a moderate adverse pressure gradient (APG, beta = 1.45) is performed to explore the contribution of large scales to the skin friction, where beta is the Clauser pressure gradient parameter. The Reynolds number based on the momentum thickness develops from Re-theta approximate to 110 to 6000 with an equilibrium region in Re-theta = 4000-5500. The spanwise wavelength (lambda(z)) spectra of the streamwise and spanwise velocity fluctuations show that the large-scale energy is significantly enhanced throughout the boundary layer. We quantify the superposition and amplitude modulation effects of these enhanced large scales on the skin friction coefficient (C-f) by employing two approaches: (i) spanwise co-spectra of < v omega(z)> and <-w omega(y)> ; (ii) conditionally averaged < v omega(z)> and <-w omega(y)>. The velocity-vorticity correlations < v omega(z)> and <-w omega(y)> are related to the advective transport and the vortex stretching, respectively. Although < v omega(z)> negatively contributes to C-f, the positive contribution of the large scales (lambda(z) > 0.5 delta) is observed in the co-spectra of weighted < v omega(z)>. For the co-spectra of weighted <-w omega(y)>, we observe an outer peak at lambda(z) approximate to 0.75 delta and the superposition of the large scales in the buffer region, leading to the enhancement of C-f. The magnitude of < v omega(z)> and <-w omega(y)> depends on the large-scale streamwise velocity fluctuations (u(L)). In particular, the negative-u(L) events amplify < v omega(z)> in the outer region, and <-w omega(y)> is enhanced by the positive-u(L) events. As a result, the skin friction induced by < v omega(z)> and <-w omega(y)> increases in the present APG TBL.