The turbulence boundary of a temporal jet

Abstract

We examine the structure of the turbulence boundary of a temporal plane jet at $Re=5000$ using statistics conditioned on the enstrophy. The data is obtained by direct numerical simulation and threshold values span 24 orders of magnitude, ranging from essentially irrotational fluid outside the jet to fully turbulent fluid in the jet core. We use two independent estimators for the local entrainment velocity $v_n$ based on the enstrophy budget. The data show clear evidence for the existence of a viscous superlayer (VSL) that envelopes the turbulence. The VSL is a nearly one-dimensional layer with low surface curvature. We find that both its area and viscous transport velocity adjust to the imposed rate so that the integral entrainment flux is independent of threshold, although low-Reynolds-number effects play a role for the case under consideration. This threshold independence is consistent with the inviscid nature of the integral rate of entrainment. A theoretical model of the VSL is developed that is in reasonably good agreement with the data and predicts that the contribution of viscous transport and dissipation to interface propagation have magnitude $2 v_n$ and $-v_n$, respectively. We further identify a turbulent core region (TC) which is a region that shrinks over time and a buffer region connecting the VSL and the TC that grows in time and where the inviscid enstrophy production is important. The BR shows many similarities with the turbulent-nonturbulent interface (TNTI), although the TNTI seems to extend into the TC. The average distance between the TC and the VSL, i.e.\ the BR thickness is about 10 Kolmogorov length scales or half a Taylor length scale, indicating that intense turbulent flow regions and viscosity-dominated regions are in close proximity.