Momentum and scalar transport at the turbulent/non-turbulent interface of a jet

Abstract

Conditionally sampled measurements with particle image velocimetry (PIV) of a turbulent round submerged liquid jet in a laboratory have been taken at Re = 2 × 10 3 between 60 and 100 nozzle diameters from the nozzle 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. 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 centreline. 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 by Mathew & Basu (Phys. Fluids, vol. 14, 2002, pp. 2065-2072 in showing that for a jet flow (without forcing) 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. (Turbulent jets differ greatly from the free shear layer in this respect.) 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, following Hunt, Eames & Westerweel (in Proc. of the IUTAM Symp. on Computational Physics and New Perspectives in Turbulence, ed. Y. Kaneda, vol. 4, 2008, pp. 331-338, Springer), are proposed for how the vortex sheet develops, 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. † Email address for correspondence: j.westerweel@tudelft.nl

Droplet growth in warm turbulent clouds

“…The terms 'engulfment' and 'nibbling' have also been used more loosely to describe essentially large-scale or small-scale motions respectively. Laboratory experiments (Westerweel et al, 2009) and numerical simulations (Mathew and Basu, 2002) of entrainment by a turbulent jet both show that the dominant process is nibbling rather than engulfing, although neither the experiments nor the simulations had the wide range of scales typical of real clouds. Because this entrainment process extends only over a limited distance, there is very little unmixed external fluid in the interior of the jet (Westerweel et al, 2009).…”

“…Laboratory experiments (Westerweel et al, 2009) and numerical simulations (Mathew and Basu, 2002) of entrainment by a turbulent jet both show that the dominant process is nibbling rather than engulfing, although neither the experiments nor the simulations had the wide range of scales typical of real clouds. Because this entrainment process extends only over a limited distance, there is very little unmixed external fluid in the interior of the jet (Westerweel et al, 2009). When additional turbulence is generated within the plume or jet, such as would result from latent heating, it has been speculated that engulfment may become more important (Westerweel et al, 2009).…”

“…Because this entrainment process extends only over a limited distance, there is very little unmixed external fluid in the interior of the jet (Westerweel et al, 2009). When additional turbulence is generated within the plume or jet, such as would result from latent heating, it has been speculated that engulfment may become more important (Westerweel et al, 2009). Indeed, dry air may penetrate the core of a cumulus cloud in so far as this picture of entrainment and mixing in cumulus is valid.…”

Pollutant Dispersion in Boundary Layers Exposed to Rural-to-Urban Transitions: Varying the Spanwise Length Scale of the Roughness

“…To provide a better view into the canopy this camera had a slight vertical inclination of 10 • , thereby eliminating the need for a Scheimpflug adapter. In order to separate the scattered light by the tracer particles (PIV) and the fluorescent signal (LIF), shortpass optical filters (PIV cameras) and a longpass optical filter (LIF camera) were employed (Westerweel et al 2009). …”

Turbulent boundary layers and channels at moderate Reynolds numbers

“…This quantity was widely used in the early days of boundarylayer research, although mostly as a means of studying the turbulent-irrotational interface, and continues to be used extensively in turbulence modelling, because the irrotational fraction strongly influences the flow behaviour (Pope 2000). The dynamics of the interface continues to be the subject of current research (Westerweel et al 2009), mostly in free shear flows, but we will restrict ourselves here to the effect of intermittency on the behaviour of the energy-containing flow scales.…”