Abstract

Spatial instability of fully developed turbulent flow in a long straight circular pipe is investigated via DNS . The incompressible Navier-Stokes equations are solved with turbulent inflow velocity field extracted from auxiliary streamwise-periodic simulation which run in parallel with the main spatial simulation. In addition, small perturbations are introduced into the inlet and velocity difference between the flows with and without perturbations is analyzed. It is shown that mean perturbation amplitude $\varepsilon$ increases exponentially with distance downstream until saturating at the level comparable to the level of turbulent fluctuations in the flow. The rate of the exponential growth is found to be constant when normalized by viscous length, $\varepsilon\sim\exp(0.002x^+)$ over the considered Reynolds number range $140\leqslant\Re_\tau \leqslant320$. The universal character of perturbation growth is confirmed also by channel flow simulations