Stretching Rate of Passive Lines in Turbulence

Abstract

The temporal evolution of passive lines in turbulence of an incompressible viscous fluid is simulated numerically for the Taylor-length Reynolds umber up to 252. The passive lines elongate in average exponentially in time. The mean exponential stretching rate γ obeys the Kolmogorov scaling law, i.e. γ = 0.17/τ _η, τ _η being the Kolmogorov time if it is estimated with chopped lines of a fixed length of O($\mathcal{L}$), $\mathcal{L}$ being the energy-containing-eddy length. However, the mean stretching rate estimated with natural (or unchopped) passive lines increases with Reynolds number more rapidly than at the rate of the Kolmogorov scaling law.