Zonal fields

The fields with m = 0 are independent of the angle tesseral fields. Some shim coils for production of tesseral and zonal fields are sketched in Fig. 2.3.2 [Krel, Mori], Room temperature shims may provide correction fields up to = 5, while cryoshims frequently provide corrections only up to n = 1. In this way homogeneities of 2 ppm can be reached over 30 cm and 5 ppm over 50 cm diameter volumes. 

The terms zonal model and flow element are also used for the simplified characterization of the flow field in a single enclosure. There, a zone represents a partial volume of air in the enclosure, whereas in the multizone models described here, a zone represents a specific enclosure which is connected to other enclosures by air conductances (see The Airflow Network later). 

A third issue is the estimates of ozone loss associated with the polar vortex. Will the Antarctic ozone hole expand and will the Arctic ozone hole begin Can the loss of ozone be better quantified, and what are the zonal asymmetries in the CIO and BrO fields How much additional ozone is lost when the polar vortex breaks up ... 

Soil classification has been oriented to soil properties in recent years, but still is tempered with concepts of soil genesis, with external associations, and with the use of the soil. The first systematic classification was by Dokuchaiev in Russia in 1882, Based upon field and laboratory characteristics, soils were grouped into three categories—normal soils of the dry-land vegetative zones and moors, transitional soils of washed or dry land sediments and abnormal soils. The system involved properties of the soil with external associations of climate and vegetation. Later, an associate (Sibirtsev) renamed the highest classes zonal intrazonal, and azonal. 

Figure 8.1. Illustration of zonal separation executed by an applied field (e.g., electrical) without flow.

While the random walk model employed here is widely applicable to F(+) methods, it fails if the molecules do not transfer rapidly between velocity states, equivalent to many random steps. Such a limitation applies to electrodecantation (noted below), where the distances are too great for rapid diffusional exchange. The random walk model is most meaningful for zonal separation methods such as chromatography and field-flow fractionation. 

Zonal (or band) electrophoresis is the simplest form of electrophoretic separation in this, the sample is applied in a small volume to the carrier gel or film and on application of the electrical field the various components in the sample are transported with their characteristic mobilities producing discrete bands or zones, more or less well separated from one another (Figure 4-20). 

Figure 9 Middle-Late Miocene timescale indicating relationships among fossil-based, radiometric and magnetic field reversal chronometries. Note that three zone successions based on developments among planktic foraminiferans are indicated. These three different zonal sequences reflect hiogeographic provincialism in these organisms. That provincialism resulted from ocean surface-water temperature differences. The calcareous nannoplankton or coccohthophore zonal scales of two different specialists are shown. These reflect different...

Cells in aqueous suspension preferably are separated by physical methods under well-defined experimental conditions rather than by chemical modification that influences cellular viability or initiates cellular processes. Moderate physical forces and short separation time gready contribute to cellular integrity. In this chapter, the application of density gradient electrophoresis to the separation of mammalian cells is described. This process may be defined as the differential zonal movement of cellular particles of anionic character suspended in a stabilized liquid column under the influence of an external electrical field so that collection of differentially moved zones is feasible. 

Figure 1-6 illustrates the mean zonal wind field for the northern hemisphere. The situation in the southern hemisphere mirrors that of the northern, although not quantitatively. In midlatitudes the dominant wind direction is from west to east, with maximum velocities in the vicinity of the subtropical jet stream near 30° latitude. The location of the polar jet stream associated with the polar front is more diffuse, and it does not show up in the averaged wind field. The westerlies encircle the globe in a wave-like... 

Finally, the medium is to be discretized spatially to perform the numerical calculations. It is preferable to employ the same discretization for radiative transfer calculations as for flow and other scalar field calculations. This is a very time-consuming approach if, for example, the zonal method is used. The multiflux approximations are more useful for this type of discretization. 

Above the range of altitudes where the QBO dominates the tropical circulation ( 35 km), a semiannual oscillation (SAO) is present in the zonal-mean zonal wind field. The average behavior of the SAO is shown in Fig. 11, which is a composite of rocketsonde observation taken over several years in the 1970s. One important difference between the SAO and the QBO is that the former has a regular period of 6 months, whereas the QBO has an irregular period, as we have seen. The regular behavior of the SAO is known to be governed by the influence of the seasonal cycle in the tropics. 

Because wave propagation and dissipation is a crucial feature of stratospheric dynamics, it is also convenient to distinguish between zonal-mean fields and perturbations thereto ... 

We will consider separately the equations that govern the zonal-mean flow and the eddies. To obtain zonal-mean and eddy equations, all variables in the equations of motion and thermodynamics are decomposed as in (4) zonal averaging of the results then produces the zonal-mean governing equations. Subtraction of the latter from the equations for the total fields yields the equations that govern the behavior of the eddies. 

The analytical approach used in Section IV.A.2 is not applicable to the tropical circulations, even though these are low-frequency phenomena, with time scales comparable to or longer than that of the extratropical circulation. The weakness of the Coriolis force in the tropics tends to decouple the zonal and meridional wind fields, so even at very low frequencies the EP-flux divergence acts mainly... 

The second inequality determines the scale of the waves that can propagate vertically in winter, when the zonal-mean zonal wind is eastward (u >0). For example, the midlatitude troposphere is dominated by slow westward-moving Rossby waves with horizontal scales on the order of a few thousand kilometers that arise from instability of the tropospheric flow. However, these waves are not found in the stratosphere because their horizontal wavenumbers k = l7t/kx) are relatively large so the second inequality cannot be satisfied for typical values of u. On the other hand, very large scale waves (horizontal wavelengths of tens of thousands of kilometers) have smaller horizontal wavenumbers and can propagate into the stratosphere. This accounts for the fact that the wave field in the winter stratosphere is dominated by planetary-scale Rossby waves, with wavenumber k in the range 1-3. 

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