On the exponential decay of turbulence in a pipe*

The crisis (critical) Reynolds number, Re=1870, was numerically established as the minimum above which turbulence in turbulent puffs persists for a long time t > 1000 advective time units. We found that turbulent energy decays exponentially at subcritical Reynolds numbers in the range of 1740–1840. The decay rate is the same as that shown by Sreenivasan in 1979, but with the addition of a constant: κ=B(d-Re)³+C. It has been established experimentally and numerically that “long-lived" turbulent puffs at supercritical Re>1870 are not maintained indefinitely. It was claimed that puffs survive for quite a long time before abruptly relaminarizing (Avila et al., Annu. Rev. Fluid Mech. 55, 2023). We used the Openpipeflow Navier-Stokes solver (openpipeflow.org) to perform highly resolved direct numerical simulations in a periodic domain (50D) for Re=1880, 1900 and 1920. For all cases, the lifetimes were very long (6000 advective time units at Re=1920), but the decay was clearly exponential rather than abrupt.