Spanwise behavior of large-scale motions in turbulent minimal pipe flow

Abstract

Direct numerical simulation data from a turbulent minimal pipe flow is used to explore the spanwise behavior of large-scale motions (LSMs) at $Re_{\tau}$ = 927, 1990, and 2916. A streamwise-minimal unit with a streamwise domain length ($L_x^{+}$ = 1000) is chosen to extract the spanwise behavior of LSMs effectively, and the minimal simulation exhibits well-established spanwise organization of LSMs. The important spanwise behaviors in high Reynolds number turbulent pipe flow are the self-similarity of energy-containing motions and two outer peaks in pre-multiplied spanwise energy spectra of streamwise velocity fluctuations (u). In this present study, we observed that these behaviors are mainly arisen from the wall-attached structures. The conditional two-point correlation represents that the outer peaks in energy spectra are strongly related with attached structures. In particular, the reconstructed pre-multiplied spanwise energy spectra of $u^{2D}$, which is the time evolution of streamwise-averaged u, showed that the two outer peaks are mainly contributed by the tall and wide attached $u_{2D}$ structures ($l_y$ > 0.2). The spanwise scales of attached $u^{2D}$ structures reveal a linear growth with respect to the distance from the wall, which supports the self-similar behavior of energy-containing motions. In addition, the enhanced attached u structures have strong connection with the near-wall region, affecting the spanwise movement of near-wall structures and the near-wall turbulent kinetic energy

the top-down influence of LSMs.