Large-scale motions in turbulent minimal pipe flows at Re_τ ≈ 930, 2000 and 3000

Direct numerical simulations of turbulent minimal pipe flow at Re_τ ≈ 930, 2000 and 3000 are performed to elucidate spanwise behavior of large scales. The streamwise domain is set to L_x⁺ ≈ 1000, which corresponds to the characteristic streamwise length of near-wall streaks. The large scales of streamwise velocity fluctuations (u) are enhanced due to the periodic boundary condition with short streamwise length. In the premultiplied spanwise energy spectra of u, two outer peaks appear at λ_z/R_­ = 0.6 and 1.3 with the increase in their magnitudes compared to those observed in a long streamwise domain (L_x = 30R). The conditional two-point correlations of the large scales (λ_z­ < 0.8R) in the outer region show that the large scales penetrate close to the wall with increasing Re_τ. At Re_τ ≈ 3000, the conditional correlations of the very large scales (λ_z­ > 0.8R) coincide with each other regardless of the reference wall-normal location, indicating the spatial confinement of very large scales. This behavior enhances the energy at the large scales, which ultimately leads to the presence of the two outer peaks in the spanwise energy spectra.