Nonlinear elongated structures in the entrance region of a circular pipe*

The nonlinear evolution of free-stream vortical disturbances entrained in the entrance region of a circular pipe is investigated using asymptotic and numerical methods. Attention is

focused on the low-frequency disturbances that induce streamwise elongated structures. A pair of vortical modes with opposite azimuthal wavenumbers is used to model the free-stream

disturbances. Numerical results show the stabilising effect of nonlinearity on the intense algebraic growth of the disturbances and an increase of the wall-shear stress due to the nonlinear interactions. A parametric study is carried out to evince the effect of the Reynolds number, the streamwise and azimuthal wavelengths, and the radial length scale of the inlet disturbance on the nonlinear flow evolution. Elongated pipe-entrance nonlinear structures (EPENS) occupying the whole pipe cross section are discovered. EPENS with ℎ-fold rotational symmetry comprise ℎ high-speed streaks positioned near the wall and ℎ low-speed streaks centred around the pipe core. These distinct structures display a striking resemblance with nonlinear travelling waves found numerically and observed experimentally in fully developed pipe flow. Good agreement of our mean-flow and root-mean-square data with experimental measurements is obtained.