Temporal scaling exceptions

It turns out that turbulent diffusion can be described with Fick s laws of diffusion that were introduced in the previous section, except that the molecular diffusion coefficient is to be replaced by an eddy or turbulent diffusivity E. In contrast to molecular diffusivities, eddy dififusivities are dependent only on the phase motion and are thus identical for the transport of different chemicals and even for the transport of heat. What part of the movement of a turbulent fluid is considered to contribute to mean advective motion and what is random fluctuation (and therefore interpreted as turbulent diffusion) depends on the spatial and temporal scale of the system under investigation. This implies that eddy diffusion coefficients are scale dependent, increasing with system size. Eddy diffusivities in the ocean and atmosphere are typically anisotropic, having much large values in the horizontal than in the vertical dimension. One reason is that the horizontal extension of these spheres is much larger than their vertical extension, which is limited to approximately 10 km. The density stratification of large water bodies further limits turbulence in the vertical dimension, as does a temperature inversion in the atmosphere. Eddy diffusivities in water bodies and the atmosphere can be empirically determined with the help of tracer compounds. These are naturally occurring or deliberately released compounds with well-estabhshed sources and sinks. Their concentrations are easily measured so that their dispersion can be observed readily. 

The second regime is characterized by approximately the same aggregate and reactive medium densities and for it scaling is described by the Eq. (31). The relation between N and Q within the frameworks of irreversible aggregation models is described as follows. The temporal evolution of Rg in the model DLA cluster-cluster can be described by the Eq. (70) of Chapter 1. For the considered case all parameters excepting c, t and which in the Eq. (70) of Chapter 1 right-hand part can be accepted as constant ones and then [44] ... 

The temporal dispersion is typically a constant contributor to At (i.e., independent of m/z), however, the contribution of spatial and velocity dispersions to At scales with m/z. The initial dispersions are typically uncorrelated so their effects add in quadrature. It is usual that the temporal dispersion is small compared to the others except at very low m/z and therefore it has an insignificant effect on resolution at higher masses. Therefore, the resolution of a TOF mass... 

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