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| Titel |
Eddy diffusion coefficients and their upper limits based on application of the similarity theory |
| VerfasserIn |
M. N. Vlasov, M. C. Kelley |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
0992-7689
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| Digitales Dokument |
URL |
| Erschienen |
In: Annales Geophysicae ; 33, no. 7 ; Nr. 33, no. 7 (2015-07-23), S.857-864 |
| Datensatznummer |
250121221
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| Publikation (Nr.) |
 copernicus.org/angeo-33-857-2015.pdf |
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| Zusammenfassung |
| The equation for the diffusion velocity in the mesosphere and the lower
thermosphere (MLT) includes the terms for molecular and eddy diffusion. These
terms are very similar. For the first time, we show that, by using the
similarity theory, the same formula can be obtained for the eddy diffusion
coefficient as the commonly used formula derived by Weinstock (1981). The latter
was obtained by taking, as a basis, the integral function for diffusion
derived by Taylor (1921) and the three-dimensional Kolmogorov kinetic energy spectrum. The
exact identity of both formulas means that the eddy diffusion and heat
transport coefficients used in the equations, both for diffusion and thermal
conductivity, must meet a criterion that restricts the outer eddy scale to
being much less than the scale height of the atmosphere. This requirement is
the same as the requirement that the free path of molecules must be much
smaller than the scale height of the atmosphere. A further result of this
criterion is that the eddy diffusion coefficients Ked, inferred
from measurements of energy dissipation rates, cannot exceed the maximum
value of 3.2 × 106 cm2 s−1 for the maximum value of
the energy dissipation rate of 2 W kg−1 measured in the mesosphere and the lower
thermosphere (MLT). This
means that eddy diffusion coefficients larger than the maximum value
correspond to eddies with outer scales so large that it is impossible to use
these coefficients in eddy diffusion and eddy heat transport equations. The
application of this criterion to the different experimental data shows that
some reported eddy diffusion coefficients do not meet this criterion. For
example, the large values of these coefficients
(1 × 107 cm2 s−1) estimated in the Turbulent Oxygen
Mixing Experiment (TOMEX) do not correspond to this criterion. The
Ked values inferred at high latitudes by Lübken (1997) meet this
criterion for summer and winter polar data, but the Ked values
for summer at low latitudes are larger than the Ked maximum value
corresponding to the criterion. Analysis of the experimental data on
meteor train observations shows that energy dissipation with a small rate of
about 0.2 W kg−1 sometimes can induce turbulence with eddy scales very
close to the scale height of the atmosphere. Our results also explain the
discrepancy between the large cooling rates calculated by Vlasov and
Kelley (2014) and the
temperatures given by the MSIS-E-90 model because, in these cases, the
measured eddy diffusion coefficients used in calculating the cooling rates
are larger than the maximum value presented above. |
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