Turbulent Jets and Wall Jets in Uniform Streaming Flow

Patel, Rajni P.

doi:10.1017/s0001925900005874

Cited by 28 publications

(20 citation statements)

References 6 publications

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“…Unlike the entrainment constants, these rates also agree quite well for nonbuoyant and buoyant flows on one hand, and for plane and axisymmetric shear flows on the other [11]. We noticed that the origin of the diffusion approach appears to be getting lost, Patel [4] already referred to Abramovich [3] as attributing it to Prandtl. In this study we show that the diffusion model is particularly suitable for forced plumes flowing down an incline. In the aquatic environment such flows can arise when the flow is released into an aquifer under some pressure to enhance dilution.…”

supporting

confidence: 53%

“…More recent experiments show that E = dH/dx for free plumes is about 0.15 [11]. Results for wall jets in a uniform stream by Patel [4] indicate that dH/dx = 0.091 for these flows. Similar to what is found for free shear flows, this widening rate is again in excellent agreement with the value of E = dH/dx = 0.095 ± 0.005 for wall plumes obtained by Grella and Faeth [26].…”

Section: Velocity-based Width Scales For Free Shear Flows and Gravitymentioning

confidence: 99%

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Mass-based depth and velocity scales for gravity currents and related flows

2008

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Gravity driven flows on inclines can be caused by cold, saline or turbid inflows into water bodies. Another example are cold downslope winds, which are caused by cooling of the atmosphere at the lower boundary. In a well-known contribution, Ellison and Turner (ET) investigated such flows by making use of earlier work on free shear flows by Morton, Taylor and Turner (MTT). Their entrainment relation is compared here with a spread relation based on a diffusion model for jets by Prandtl. This diffusion approach is suitable for forced plumes on an incline, but only when the channel topography is uniform, and the flow remains supercritical. A second aspect considered here is that the structure of ET's entrainment relation, and their shallow water equations, agrees with the one for open channel flows, but their depth and velocity scales are those for free shear flows, and derived from the velocity field. Conversely, the depth of an open channel flow is the vertical extent of the excess mass of the liquid phase, and the average velocity is the (known) discharge divided by the depth. As an alternative to ET's parameterization, two sets of flow scales similar to those of open channel flows are outlined for gravity currents in unstratified environments. The common feature of the two sets is that the velocity scale is derived by dividing the buoyancy flux by the excess pressure at the bottom. The difference between them is the way the volume flux is accounted for, which-unlike in open channel flows-generally increases in the streamwise direction. The relations between the three sets of scales are established here for gravity currents by allowing for a constant co-flow in the upper layer. The actual ratios of the three width, velocity, and buoyancy scales are evaluated from available experimental data on gravity currents, M. Princevac 123 370 Environ Fluid Mech (2009) 9:369-387and from field data on katabatic winds. A corresponding study for free shear flows is referred to. Finally, a comparison of mass-based scales with a number of other flow scales is carried out for available data on a two-layer flow over an obstacle. Mass-based flow scales can also be used for other types of flows, such as self-aerated flows on spillways, water jets in air, or bubble plumes.

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supporting

confidence: 53%

Section: Velocity-based Width Scales For Free Shear Flows and Gravitymentioning

confidence: 99%

Mass-based depth and velocity scales for gravity currents and related flows

2008

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“…A combination of both models was proposed by Jirka [7]. We also noticed that the origin of the diffusion concept appears to be getting lost, Patel [9] already quoted Abramovich [3] as attributing it to Prandtl. The two concepts are compared for plane jets and plumes in Sect.…”

Section: Introductionmentioning

confidence: 72%

“…Prandtl's diffusion relation can also be restated in terms of top-hat scales. In the spirit of Patel [9] and [26] the corresponding relation can be stated as…”

Section: Relation Between the Diffusion And Entrainment Conceptsmentioning

confidence: 99%

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Alternative depth-averaged models for gravity currents and free shear flows

2010

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Two approaches have traditionally been used to describe the widening rate of jets and plumes: the diffusion concept of Prandtl, and the entrainment principle of Morton, Taylor and Turner. The entrainment concept is based on depth-averaged flow scales, and was later applied to plane gravity currents on an incline by Ellison and Turner [ET]. The two parameterizations are compared here for free shear flows, and gravity currents. It is shown that the diffusion concept is suitable for supercritical gravity currents, and that both approaches agree for subcritical ones. Depth-averaged models are also used for open channel flows, but the depth and velocity scales for the two flows are different. Those of ET are derived from the velocity distribution, whereas the depth of an open channel flow is the vertical extent of the dense liquid phase, and the velocity is derived from its flux. To reconcile the two descriptions, we extended the mass-based flow scales of open channel flows to gravity currents in an earlier contribution. In the present study these scales are outlined, and extended further to axisymmetric and non-buoyant free shear flows. Ratios of the diffusion rates in terms of mass-and velocity-based flow scales, are obtained from available experimental data for free shear flows.

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