Influences of Large-scale Structures on Skin Friction in an Adverse Pressure Gradient Turbulent Boundary Layer

Direct numerical simulation (DNS) of a turbulent boundary layer (TBL) subjected to adverse pressure gradient (APG) at Reτ = 834 is performed to investigate large-scale influences on vortical motions. For comparison, DNS data of a zero pressure gradient (ZPG) TBL at Reτ = 837 is analyzed. The spanwise energy spectra of the streamwise velocity fluctuations show that the large-scale energy above 400 z    (λz/δ ≈ 0.5) is significantly enhanced in the APG TBL. Large-scale streamwise velocity fluctuations (uL) is extracted by employing a long-wavelengthpass filter with a cut-off wavelength of 400. z    Two velocityvorticity correlations ( z v   and ), y w   which represent the advective vorticity transport and vortex stretching, respectively, are conditionally averaged with respect to uL to explore the extension of large-scale influences on the vortical motions. The velocity-vorticity correlations are directly related to the skin friction coefficient (Cf). The total Cf in the APG TBL is reduced by 28% from that in the ZPG TBL. The skin friction induced by z v   and y w   contribute negatively and positively to the total Cf respectively. In the APG TBL, the negative contribution of z v   decreases 29.6%, while the positive contribution of y w   slightly increases about 7.0%. Under the intense negative and positive uL ( 2 L u    and 2), L u    the contribution of z v   in the APG TBL is enhanced 8.33 and 2.72 times compared to the ZPG TBL. The skin friction induced by y w   increases 1.8 times only under 2 L u    in the APG TBL. The enhanced largescale motions in the outer region strongly modulate the vortical motions. In particular, the low-speed structures augment the contribution of the advective vorticity transport and the contribution of the vortex stretching is enhanced under the influence of the high-speed structures in the APG TBL. INTRODUCTION One of important features in APG TBLs is an increase of large scales in the outer region: e.g., a strong secondary peak in the premultiplied energy spectra of the streamwise velocity fluctuations (Harun et al. 2013; Lee 2017). Large-scale structures (LSSs), scale with Ο (δ), where δ is the boundary layer thickness, play an important role in the production of turbulent kinetic energy and the transport of momentum. LSSs contain about half of the turbulent kinetic energy and Reynolds shear stress in turbulent flows (Guala et al. 2006; Balakumar & Adrian 2007). LSSs with strong energy in the outer region extend to the near-wall region as footprints (Hutchins & Marusic 2007a). Hutchins & Marusic (2007b) observed that amplitudes of three velocity fluctuations and the Reynolds shear stress are attenuated under negative largescale fluctuations at y+ = 15 in the instantaneous fluctuating signals. To measure a degree of amplitude modulation (AM) influences, Mathis et al. (2009) introduced AM coefficient, which is the correlation between the large-scale fluctuations and filtered envelope of small-scale fluctuations. Using the AM coefficient, the AM influences of LSSs on small scales were investigated for the streamwise velocity fluctuations (Mathis et al. 2009) and for the cross-stream components (Talluru et al. 2014). Since the outer energy carried by the large scales is enhanced in APG TBLs, the degree of the AM for the streamwise components is enhanced compared to ZPG TBLs (Harun et al. 2013; Lee 2017). Given that the footprints of large-scales low-speed structures is narrower than that of the low-speed structure (Hwang et al. 2016), the influence of outer large-scale lowand high-speed structures is asymmetric in the near-all region (Agostini & Leschziner 2014; Hwang et al. 2016). This difference is related to the near-wall spanwise motions induced by the associated largescale circulations, which are congregative and dispersive (Hwang et al. 2016). Ganapathisubramani et al. (2012) statistically investigated the AM influences on the small-scale streamwise velocity fluctuations with respect to the strength of large scales and showed that the amplitude of the small scales in the near-wall region is attenuated or amplified under the negative of positive large scales, respectively. Since the near-wall vortical structures are related to the small-scale velocity fluctuations, the vortical motions could be affected by the outer large-scale structures and thus the large-scale influences on the vortical motions could be enhanced in APG TBLs. Recently, Yoon et al. (2016a) derives an expression for the skin friction coefficient (Cf), which quantifies the contributions of the velocity-vorticity correlations ( z v   and ) y w   to the skin friction. The correlations z v   and y w   are interpreted as the advective vorticity transport and vortex stretching (Tennekes & Lumley 1972). The streamwise vortical structures are a major part of the self-sustaining process since they create or amplify the near-wall streaks via the lift-up process (Kim 2011). Although the vortical motions play a crucial role in near-wall turbulence, most studies in the APG TBLs have not dealt with the influences of LSSs on the vortical motions. In the APG TBL, the streamwise