Scale height

If we define a molecular weight for each constituent, then we can rearrange equation (1). 

The abundance of light elements at high altitude leads to a finite flux of these substances escaping the Earth s gravitational field. This results from a combination of a very long mean free path and a few particles having the requisite escape velocity due to the high velocity tail of the Boltzmann velocity distribution. 

In terms of relevance to biogeochemical cycling, most of our emphasis is placed on the so-called homosphere (which really is homogeneous only with respect to N2, O2, Ar, and other long-lived gases). 

In the case of a mixed atmosphere, M cannot be defined precisely since the composition is variable (especially due to water vapor). If dry air is assumed (which is a good approximation most of the time at altitudes above about 5 km), then M = 28.97g/mol. If the atmosphere is assumed to be roughly isothermal, then from equation (5) pressure falls off with altitude as  

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Figure 13-5 is the box model of the remote marine sulfur cycle that results from these assumptions. Many different data sets are displayed (and compared) as follows. Each box shows a measured concentration and an estimated residence time for a particular species. Fluxes adjoining a box are calculated from these two pieces of information using the simple formula, S-M/x. The flux of DMS out of the ocean surface and of nss-SOl back to the ocean surface are also quantities estimated from measurements. These are converted from surface to volume fluxes (i.e., from /ig S/(m h) to ng S/(m h)) by assuming the effective scale height of the atmosphere is 2.5 km (which corresponds to a reasonable thickness of the marine planetary boundary layer, within which most precipitation and sulfur cycling should take place). Finally, other data are used to estimate the factors for partitioning oxidized DMS between the MSA and SO2 boxes, for SO2 between dry deposition and oxidation to sulfate, and for nss-SO4 between wet and dry deposition. 

Abstract. The Milky Way harbours two disks that appear distinct concerning scale-heights, kinematics, and elemental abundance patterns. Recent years have seen a surge of studies of the elemental abundance trends in the disks using high resolution spectroscopy. Here I will review and discuss the currently available data. Special focus will also be put on how we define stars to be members of either disk, and how current models of galaxy formation favour that thick disks are formed from several accreted bodies. The ability for the stellar abundance trends to test such predictions are discussed. 

The rate of photolysis, J, depends on the absorption cross-section, a, the number density, the scale height and the angle, all of which are unique properties of a planetary atmosphere. For the Earth and the Chapman mechanism for ozone the O3 concentration maximum is 5 x 1012 molecules cm-3 and this occurs at 25 km, shown in Figure 7.12, and forms the Chapman layer structure. 

Radiative heating Scale height Chapman layers... 

A probe making a descent onto an extra solar planet measures the local acceleration due to gravity as 10.0 ms 2 and the scale height as 11.43 km. 

Scale height The presence of an atmosphere leads to the analogous concepts of scale height... 

The effective surface temperature of Titan is 98 K and the atmosphere is nearly completely nitrogen. Calculate the scale height for Titan s atmosphere. Comment on the diurnal variation of the scale height and the variation with altitude. 

Scale height The decay constant assuming an exponential decay in pressure and temperature with height in a planet s atmosphere. 

In Section I, we mentioned that the TFM can simulate fluidized beds at engineering scales (height 1-2 m), and that the large-scale industrial fluidized-bed reactors (diameter 1-5m, height 3-20m) are still far beyond its capabilities. Clearly, it would be highly desirable to predict the properties of gas-solid flows at the industrial scale however at present, there is no fully evolved model— based on fundamental principles—which is capable of this. In this section, we outline some new ideas in this direction that have been developed both at the... 

The predictions of the various expressions for in the neutral case are shown in Fig. 9, where the scale height has been replaced with... 

Substituting this result into Eq. (9.12) and defining the scale height to be H, the vertical diffusivity variation is... 

The form and magnitude of the scale height H clearly depends on the meteorological conditions. Wyngaard (1975) concluded that turbulence is confined to a layer of thickness H given approximately by... 

In Figure 1, we present the luminosity functions obtained with the assumptions of total miscibility (full line) and total separation (dashed line) for an age of the Galactic disk of 15 10 years. These luminosity functions take into account the increase of the vertical scale height over the plane of the disk with the age of the objects. This geometrical effect [2] nearly suppress the bump at L 10-4 Lq which would have been produced by the strong decrease of the cooling rate in the case of total separation [3]. 

The convective turbulence tend to dissipate large scale shears (wave length a > pressure scale height H ). The rate of dissipation... 

Our set of model photospheres, as defined by the above conditions, can be essentially characterized by three free parameters (In addition to t-tQ), in much the same way as stellar photospheres. These are an effective temperature T, a scale height AR, and the effective abundance Z, defined by the relations... 

Figure 1. The total optical depth at three wavelengths is plotted versus the total hydrogen number density. The extent of the photosphere is indicated by the solid portion of the curves. A radial distance equal to the scale height is also shown.

From these results, we construct Table 1, which provides a quantitative measure of the location and thickness of the photospheric region. Of special interest are the last two rows, giving the radial extent of the photosphere as a fraction of the scale height AR and the radius of the photosphere on March 1 (as determined in the... 

Equation (4) only describes the anisotropy due to the geometry and the opacity distribution, but not that introduced by the scale height of the source function. This means that the accuracy of the solutions obtained by the method proposed here improves when temperature gradients are smouth or/and scattering is dominant. The accuracy, in the worst case, for a supernovalike envelope is better than lOX in J for r[Pg.437]

Values of Wp for particle-associated chemicals are generally in the range 105 to 106 (Eisenriech et al., 1981 Bidleman, 1988). A value of W = 10s is calculated to result in a residence time for chemicals due to wet deposition in the well-mixed troposphere (with a scale height of 7 km) of 20 days for a constant precipitation rate of 1 m yr1 (the residence time = (height of atmosphere considered)/WJ, where J is the precipitation rate). 

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