Energy-consistent entrainment relations for jets and plumes

Reeuwijk, Maarten van; Craske, John

doi:10.1017/jfm.2015.534

Cited by 105 publications

(145 citation statements)

References 40 publications

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“…We plot R/r 0 as a function of z/r 0 in figure 3 and a best fit to the data provides a value of α = 0.11±0.01, where the tolerances indicate the standard deviation within our measurements. This value falls within the range of α = {0.095, 0.15}, the median value being α = 0.12, from the six independent studies for which data are reported within van Reeuwijk & Craske (2015).…”

Section: Validation Of the Piv Datamentioning

confidence: 57%

“…As a second method for assessing the entrainment coefficient we consider the findings of van Reeuwijk & Craske (2015) in which they showed, for a time-averaged self-similar pure-plume, that α can be expressed in terms of turbulence production, energy flux and buoyancy effects. This decomposition allows a deeper physical insight of the entrainment coefficient beyond the original hypothesis provided by Morton et al (1956), i.e.…”

Section: Validation Of the Piv Datamentioning

confidence: 99%

“…More recent studies have contributed a wealth of experimental and numerical data in order to guide the parameterisation, and indeed choice, of the closure model and improve the understanding of the entrainment process (e.g. Ezzamel et al 2015;van Reeuwijk & Craske 2015). Other studies, presumably inspired by the work of Corrsin & Kistler (1955), have sought to untangle the complexities of turbulent flows by considering the entrainment and mixing across 'surfaces' within the flow.…”

Section: Introductionmentioning

confidence: 99%

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Conditional sampling of a high Péclet number turbulent plume and the implications for entrainment

et al. 2017

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We present simultaneous two-dimensional velocity and scalar measurements on a central vertical plane in a pure turbulent plume. We use an edge-detection algorithm to determine the edge of the plume, and compare the data obtained in both a fixed Eulerian frame and a frame relative to local coordinates defined in terms of the instantaneous plume edge. In an Eulerian frame we observe that the time-averaged distributions of vertical and horizontal velocity are self-similar, the vertical velocity being well represented by a Gaussian distribution. We condition these measurements on whether fluid is inside or outside of the plume, and whether fluid inside is mixed plume fluid or engulfed ambient fluid. We find that, on average, 5% of the total vertical volume transport occurs outside the plume and this figure rises to nearly 14% at heights between largescale coherent structures. We show that the fluxes of engulfed fluid within the plume envelope are slightly larger than the vertical transport outside the plume -indicating that ambient fluid is engulfed into the plume envelope before being nibbled across the turbulent/non-turbulent interface (TNTI) and then ultimately irreversibly mixed. Our new measurements in the plume coordinate (following the meandering fluctuating plume)show the flow within the plume and in the nearby ambient fluid is strongly influenced by whether an eddy is present locally within the plume, or absent. When an eddy is present and the plume is wide, the vertical velocities near the plume edge are small and hence all vertical transport is inside the plume. In regions where the plume is narrow † Email address for correspondence: h.burridge@imperial.ac.uk 2 H. C. Burridge, D. A. Parker, E. S. Kruger, J. L. Partridge and P. F. Linden and there is no eddy, large vertical velocities and hence transport are observed outside the plume suggesting that pressure forces associated with the eddies accelerate ambient fluid which is then engulfed into the plume. Finally, we show that observing significant vertical velocities beyond the scalar edge of the plume does not suggest that the characteristic width of the velocity distribution is greater than that of the scalar field; on the contrary, we show our observations to be consistent with a buoyancy distribution that is up to 20% wider than that of the velocity. Measurements in the plume coordinates show that the mixing of momentum across the plume results in a distribution for which the differential entropy is close to maximal and the mixing of momentum is uninhibited (i.e. not bounded) by the TNTI of the plume. Furthermore, our measurements suggest that the scalar mixing across the plume may also result in a distribution for which the differential entropy is close to maximal but, in contrast to the momentum, the scalar mixing is strictly bounded by the plume edge.

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Section: Validation Of the Piv Datamentioning

confidence: 57%

Section: Validation Of the Piv Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conditional sampling of a high Péclet number turbulent plume and the implications for entrainment

et al. 2017

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“…Atmosphere-Ocean Plume˙Behaviour experimental (Ezzamel et al, 2015) investigations -a good summary of which is presented by van Reeuwijk & Craske (2015).…”

Section: Resultsmentioning

confidence: 99%

The Fluxes and Behaviour of Plumes Inferred from Measurements of Coherent Structures within Images of the Bulk Flow

2016

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This paper describes how measurements of the movement of identifiable features at the edge of a turbulent plume can be interpreted to determine the properties of the mean flow and consequently, using plume theory, can be used to make estimates of the fluxes of volume (mass), momentum and buoyancy in a plume. This means that video recordings of smoke rising from a chimney or buoyant material from a source on the sea bed can be used to make accurate estimates of the source conditions for the plume. At best we can estimate the volume flux and buoyancy flux to within about 5% and 15% of the actual values, respectively. Although this is restricted to the case of a plume rising in a stationary and unstratified environment, we show that the results may be of practical use in other more complex situations. In addition, we demonstrate that large scale (turbulent) coherent structures at the plume edge form on a scale approximately 40% of the local (mean) plume half-width and travel at almost 60% of the average local (mean) velocity in the plume.

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“…Here we note a correspondence with turbulent plumes, where a ''pure'' plume will have a constant value for Ri. If the flow has an excess (deficit) of momentum at the source the plume is referred to as forced (lazy) [21,22]; the flow will adjust its own state due to the work done by gravity until it becomes pure. The evolution of Ri for the gravity current in time (Fig.…”

Section: Turbulent Entrainmentmentioning

confidence: 99%

Small-scale entrainment in inclined gravity currents

2017

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We investigate the effect of buoyancy on the small-scale aspects of turbulent entrainment by performing direct numerical simulation of a gravity current and a wall jet. In both flows, we detect the turbulent/nonturbulent interface separating turbulent from irrotational ambient flow regions using a range of enstrophy iso-levels spanning many orders of magnitude. Conform to expectation, the relative enstrophy isosurface velocity v n in the viscous superlayer scales with the Kolmogorov velocity for both flow cases. We connect the integral entrainment coefficient E to the small-scale entrainment and observe excellent agreement between the two estimates throughout the viscous superlayer. The contribution of baroclinic torque to v n is negligible, and we show that the primary reason for reduced entrainment in the gravity current as compared to the wall-jet are 1) the reduction of v n relative to the integral velocity scale u T ; and 2) the reduction in the surface area of the isosurfaces.

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Energy-consistent entrainment relations for jets and plumes

Cited by 105 publications

References 40 publications

Conditional sampling of a high Péclet number turbulent plume and the implications for entrainment

Conditional sampling of a high Péclet number turbulent plume and the implications for entrainment

The Fluxes and Behaviour of Plumes Inferred from Measurements of Coherent Structures within Images of the Bulk Flow

Small-scale entrainment in inclined gravity currents

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