Buoyancy flux parameter

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. 

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

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 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) ... 

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. 

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. 

By definition the Monin-Obukhov length is the height at which the production of turbulence by both mechanical and buoyancy forces is equal. The parameter L, like the flux Richardson number, provides a measure of the stability of the surface layer. As we discussed, when Rf > 0 and therefore according to (16.69) L > 0 the atmosphere is stable. On the other hand, when the atmosphere is unstable, Rf < 0 and then L < 0. Because of the inverse relationship between Rf and L, an adiabatic atmosphere corresponds to very small (positive or negative) values of Rf and to very large (positive or negative) values of L. Typical values of L for different atmospheric stability conditions are given in Table 16.2. 

Equation (3) forms the basis for the parameterization of surface fluxes in all models of atmospheric circulations. This approach can be generalized to account for heat fluxes that are accompanied by buoyant acceleration of fluid elements. In this case, a must be replaced by a function where is a nondimensional parameter that measures the relative contributions of buoyancy and mechanically induced effects on fluid accelerations. Further extensions to account for a variety of other effects (most notably surface heterogeneity) not included in the formulation above are invariably also based on elaborations of (3) and remain an active area of research (Fairall et al., 2003). 

FIG. 9. Correlation of heat transfer data for large x/D in terms ofNusselt number ratio and buoyancy parameter for (a) uniform wall heat flux, (b) uniform wall temperature... 

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