Buoyancy flux

For most plume rise estimates, the value of the buoyancy flux parameter F in m s is needed. 

Assuming that the buoyancy flux parameter F is greater than 55 in both situations, what is the proportional final plume rise for stack A compared to stack B if A has an inside diameter three times that of B ... 

The SCREEN model calculates plume rise for flares based on an effective buoyancy flux parameter. An ambient temperature of 293° K is assumed in this calculation and therefore none is input by the user. It is assumed that 55 percent of the total heat is lost due to radiation. 

These effective stack parameters are somewhat arbitrary, but the resulting buoyancy flux estimate is expected to give reasonable final plume rise estimates for flares. However, since building downwash estimates depend on transitional momentum plume rise and transitional buoyant plume rise calculations, the selection of effective stack parameters could influence the estimates. Therefore, building downwash estimates should be used with extra caution for flare releases. 

The use of the methods of Briggs to estimate plume rise are relied on in the SCREEN model. Stack tip downwash is estimated following Briggs (1973, p.4) for all sources except those employing the Schulman-Scire downwash algorithm. Buoyancy flux for non-flare point sources is calculated from ... 

Relationship between buoyancy flux and pollutant flux ... 

From source heat flux q, the buoyancy flux F Is... 

The presence of a lithosphere with a thickness up to 100 km above the plume head obscures observations that could be made in terms of heat flow, gravity field or seismic structure. Establishing the temperature and flow fields beneath a hotspot thus becomes a difficult exercise. Several key parameters (Fig. 2) are poorly constrained and mostly result from theoretical fluid dynamics model, which underlines their large uncertainty. The temperature anomaly within the hotspot region is generally estimated to be approximately 200 100°C with large uncertainties (Shilling 1991 Sleep 1990). These temperature anomalies will induce smaller densities in the plume and the flux of the density anomalies is called buoyancy flux as defined in (Sleep 1990) ... 

Where ju is the viscosity. It follows that the buoyancy flux 5(= ApQ is proportional to the square of the average upwelling velocity in the pipe ... 

For the range of buoyancy fluxes found in mantle plumes (0.5-11 M g s ), the mantle upwelling velocities should vary by a factor of 3-4. This was shown by Bourdon et al. (1998) to be consistent with the range in °Th- U and disequilibrium found... 

In [13], based on a one-dimensional model, it was shown that the observed parameters of the NBML in the Black Sea are defined by the buoyancy fluxes balance between the destabilizing geothermal heat flux and stabilizing salt flux supplied with the waters of the Sea of Marmara penetrating to great depths. 

If a waste source emits a gas with a buoyancy flux of 50m /s, and the wind averages 4m/s, find the plume rise at a distance of 750 m downward from a stack that is 50 m high under unstable atmospheric conditions. Use the equation proposed by Briggs. 

The turbulent diapycnal exchange coefficient in stratified water can be estimated according to Osborne (1980) assuming a balance between the production of turbulent kinetic energy, the buoyancy flux, and the dissipation of mrbulent kinetic energy... 

It is illuminating to study the time evolution of a river plume as an initial value problem. It can be shown that the current pattern is governed by a geostrophically adjusted eddy confined to the buoyancy patch (near field) and a coastally trapped flow that develops in the wake of a Kelvin wave (far field). Behind the front of the first Kelvin wave mode, undercurrents are set up. Although the velocities of the flow forced by the momenrnm of the river mnoff are small enough to justify a linear treatment, there are important nonlinear effects owing to the advection of density, which limits the validity of the linear analytical models. In particular, the structure of the near field in front of the river mouth is dominated by the response to the buoyancy flux associated with the river discharge. 

Figure 5. He/ He vs. (a-left) buoyancy flux, (b-opposite page, upper) Lithosphere age. (e-opp. page, lower) Plate speed. Points show the highest e/" He ratios at eaeh island with dashed lines extending to the lowest values. Only crushing analyses are used to avoid post-eruptive addition of cosmogenie e and radiogenic ""He. Buoyancy flux is taken direetly from Davies (1988) or ealeulated from Sleep (1990) assuming an excess plume temperature of 200°C. He data are from Kurz et al. (1982a, 1983) for Gough, Tristan da Cunha and Hawaii Hilton et al.

Overview. There does not seem to be any direct relationship between plate speed or plume flux and the value of He/" He measured at ocean islands. It does seem possible that somewhat more variable He/" He ratios may be found on old oceanic lithosphere or near continental margins/subduction zones, but this cannot be firmly concluded based on the available evidence (Fig. 5). Buoyancy flux, plate speed and lithosphere age may serve to modulate the He/" He signal at ocean islands, but it is clear that they do not control it. 

The residual depleted mantle (RDM) has a constant volume, which is a free parameter. Mass outflow is specified from plume buoyancy fluxes. The mass inflow contains He and U, with concentrations related to those of the bulk mantle by specified small enrichment factors operating during formation of oceanic lithosphere. The present He/ He ratio is the highest seen at Loihi, while the starting value is solar. 

In the formula, is the gustiness wind speed, w, is the characteristic scale of the free convection velocity, is the empirical constant, its order is 1.0, usually takes 1.25 (Fairall, 1996), Fj is the buoyancy flux terms, which reflects the turbulent fluctuations, w T is the vertical flux of the virtual temperature, z, is the mixing height in the troposphere. 

The eqrrations under subsections 1 and 2 following are recommended for plumes dominated by buoyancy. The buoyancy flux parameter is defined as... 

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