Momentum and Scalar Transport at the Turbulent/Non-Turbulent Interface of a Jet

A longstanding question about unconfined, but localised, turbulent flows is to describe and quantify the characteristic features of the inhomogeneous transition zone between fully developed turbulence and the decaying fluctuations outside the turbulent region. Recent findings indicate the existence of a finite jump in the tangential velocity at the interface. This is associated with small-scale eddying motion at the outward propagating interface (nibbling) by which irrotational fluid becomes turbulent.

In order to investigate the dynamics and transport processes at the continuous, and well defined bounding interface between the turbulent and non-turbulent regions of flow, conditionally sampled measurements with particle

image velocimetry (PIV) of a turbulent round submerged liquid jet have been taken at Re = 2000. The jet carries a fluorescent dye measured with planar laser-induced fluorescence (LIF), and the surface discontinuity in the scalar concentration is identified as the fluctuating turbulent jet interface. Thence the mean outward ‘boundary entrainment' velocity is derived and shown to be a constant fraction (about 0.07) of the the mean jet velocity on the centerline. Profiles of the conditional mean velocity, mean scalar, and momentum flux show that at the interface there are clear discontinuities in the mean axial velocity and mean scalar, and a tendency towards a singularity in mean

vorticity. These actual or asymptotic discontinuities are consistent with the conditional mean momentum and scalar transport equations integrated across the interface. Measurements of the fluxes of turbulent kinetic energy and enstrophy are consistent with computations in showing that for a jet flow the entrainment process is dominated by small scale eddying at the highly sheared interface (‘nibbling'), with large scale engulfing making a small (less than 10%) contribution consistent with concentration measurements showing that the interior of the jet is well mixed. To explain the difference between velocity and scalar profiles, their conditional mean gradients are defined in terms of a local eddy viscosity and eddy diffusivity and the momentum and scalar fluxes inside the interface. Since the eddy diffusivity is larger than

the eddy viscosity, the scalar profile is flatter inside the interface so that the scalar discontinuity is relatively greater than the mean velocity discontinuity.

Theoretical arguments are proposed for how the vortex sheet

develops and how the internal structure of the interface layer relates to the inhomogeneous rotational and irrotational motions on each side, and why the dominant entrainment process of jets and wakes differs from that of free shear layers.