Virtual origin correction for lazy turbulent plumes

Hunt, Gary R.; Kaye, Nigel B.

doi:10.1017/s0022112001003871

Cited by 199 publications

(193 citation statements)

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“…The self-similar growth of the turbulent puff leads to r = ↵s, where r is the half-width of the cloud and s the distance from the source (see figure 1a). In reality, details of source conditions displace the effective origin of the cloud relative to the piston (Hunt & Kaye 2001). The virtual origin can be computed by extrapolating the measured r against s plot, as illustrated in figure 7. .…”

Section: Analogue Experimentsmentioning

confidence: 99%

Violent expiratory events: on coughing and sneezing

2014

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Violent respiratory events such as coughs and sneezes play a key role in transferring respiratory diseases between infectious and susceptible individuals. We present the results of a combined experimental and theoretical investigation of the fluid dynamics of such violent expiratory events. Direct observation of sneezing and coughing events reveals that such flows are multiphase turbulent buoyant clouds with suspended droplets of various sizes. Our observations guide the development of an accompanying theoretical model of pathogen-bearing droplets interacting with a turbulent buoyant momentum puff. We develop in turn discrete and continuous models of droplet fallout from the cloud in order to predict the range of pathogens. According to the discrete fallout model droplets remain suspended in the cloud until their settling speed matches that of the decelerating cloud. A continuous fallout model is developed by adapting models of sedimentation from turbulent fluids. The predictions of our theoretical models are tested against data gathered from a series of analogue experiments in which a particle-laden cloud is ejected into a relatively dense ambient. Our study highlights the importance of the multiphase nature of respiratory clouds, specifically the suspension of the smallest drops by circulation within the cloud, in extending the range of respiratory pathogens.

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Section: Analogue Experimentsmentioning

confidence: 99%

Violent expiratory events: on coughing and sneezing

2014

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“…The point source theory for vertical plumes used above must therefore be modified to include finite area sources. A number of corrections have been developed (Hunt and Kaye 2001) to take into account finite area sources in the theory of turbulent entrainment. A simple estimate may be given by noticing that the angle θ of the plume's cone (Fig.…”

Section: Neutral Height Of the Sinking Plumementioning

confidence: 99%

Artificial upwelling using offshore wind energy for mariculture applications

Viúdez¹,

Balsells²,

Rodríguez-Marroyo³

2016

Sci. Mar.

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Summary: Offshore wind is proposed as an energy source to upwell nutrient-rich deep water to the ocean photic layers. A spar-buoy wind turbine with a rigid tube about 300 m long is proposed as a pipe to drive deep water up to the surface. The minimum energy required to uplift the water is the potential energy difference between surface waters inside and outside the pipe, which depends on the background density profile. The corresponding surface jump or hydraulic head, h, calculated for several analytical and experimental density profiles, is of the order of 10 cm. If the complete turbine power (of the order of several MW) is used for raising the water (assuming a 100% pump efficiency), in a frictionless flow, very large water volumes, of the order of thousands of m 3 s −1 , will be transported to the photic layers. In a more realistic case, taking into account pipe friction in wide pipes, of the order of 10 m radius, and a power delivered to the fluid of 1 MW, the volume transport is still very large, about 500 m 3 s −1 . However, such a large amount of dense water could sink fast to aphotic layers due to vertical static instability (the fountain effect), ruining the enhancement of primary production. Hence, some ways to increase the turbulent entrainment and avoid the fountain effect are proposed. From the energetic viewpoint, artificial upwelling using offshore wind energy is a promising way to fertilize large open sea regions. This mariculture application is, however, severely subjected to atmosphere and ocean climatology, as well as to ecological dynamics. The general problem is multidisciplinary, and some important physical, engineering and ecological questions need to be seriously addressed to improve our confidence in the approach presented here.Keywords: artificial upwelling; mariculture applications; ocean fertilization; offshore wind energy; spar-buoy wind turbine.Afloramiento artificial producido con energía eólica con aplicación a la maricultura Resumen: Analizamos el uso de la energía eólica marina como fuente de energía para aflorar aguas profundas ricas en nutrientes a las capas fóticas del océano. Una turbina de viento tipo boya-pértiga, con un tubo rígido de unos 300 m de largo, se propone para transportar las aguas profundas hasta la superficie. La energía mínima necesaria para elevar el agua es la diferencia de energa potencial entre las aguas superficiales dentro y fuera de la tubería, que depende del perfil de densidad de fondo. El salto superficial de agua, o cabezal hidráulico h, calculado para varios perfiles analíticos y experimentales de densidad, resulta ser del orden de 10 cm. Si la potencia total de la turbina (del orden de varios MW) se utiliza para elevar el agua (suponiendo una eficiencia de la bomba del 100%), en un flujo sin fricción, el transporte de volumen de agua transportado a las capas fóticas es muy elevado, del orden de miles de m 3 s −1 . En un caso más realista, teniendo en cuenta la fricción en tuberías de un ancho del orden de 10 m radio, y una potencia proporcionada...

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“…Region 1: independent plumes Consider two axisymmetric turbulent plumes with sources at the same height and separated by a horizontal distance x 0 . When the two plumes are independent of each other the average buoyancy profile of each single turbulent plume can be represented by a 'top hat' profile (Turner 1979) with a radius given by b(z) = (6/5)αz, where z = (z + z V ), z is the vertical distance from the source, z V is the location of the virtual origin (Hunt & Kaye 2001) and α is the entrainment constant (Morton et al 1956). The virtual origin correction is the distance from the physical source that an imaginary pure plume, with zero momentum and volume fluxes but with the same buoyancy flux issuing from the virtual origin, has in order for the actual buoyancy, momentum and volume fluxes of the plume to be the same at the physical source, and is used since the equations introduced below are strictly valid for pure plumes.…”

Section: Dynamics Of Two Coalescing Plumesmentioning

confidence: 99%

Entrainment in two coalescing axisymmetric turbulent plumes

Cenedese

Linden

2014

J. Fluid Mech.

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A model of the total volume flux and entrainment occurring in two coalescing axisymmetric turbulent plumes is developed and compared with laboratory experiments. The dynamical evolution of the two plumes is divided into three regions. In region 1, where the plumes are separate, the entrainment in each plume is unaffected by the other plume, although the two plumes are drawn together due to the entrainment of ambient fluid between them. In region 2 the two plumes touch each other but are not yet merged. In this region the total entrainment is a function of both the dynamics of the touching plumes and the reduced surface area through which entrainment occurs. In region 3 the two plumes are merged and the entrainment is equivalent to that in a single plume. We find that the total volume flux after the two plumes touch and before they merge increases linearly with distance from the sources, and can be expressed as a function of the known total volume fluxes at the touching and merging heights. Finally, we define an 'effective' entrainment constant, α eff , as the value of α needed to obtain the same total volume flux in two independent plumes as that occurring in two coalescing plumes. The definition of α eff allows us to find a single expression for the development of the total volume flux in the three different dynamical regions. This single expression will simplify the representation of coalescing plumes in more complex models, such as in large-scale geophysical convection, in which plume dynamics are not resolved. Experiments show that the model provides an accurate measure of the total volume flux in the two coalescing plumes as they evolve through the three regions.

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Virtual origin correction for lazy turbulent plumes

Cited by 199 publications

References 20 publications

Violent expiratory events: on coughing and sneezing

Violent expiratory events: on coughing and sneezing

Artificial upwelling using offshore wind energy for mariculture applications

Entrainment in two coalescing axisymmetric turbulent plumes

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