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Eddy Diffusion Coefficients and Their Upper Limits Based on Application of the Similarity Theory : Volume 33, Issue 7 (23/07/2015)

By Vlasov, M. N.

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Book Id: WPLBN0004002589
Format Type: PDF Article :
File Size: Pages 8
Reproduction Date: 2015

Title: Eddy Diffusion Coefficients and Their Upper Limits Based on Application of the Similarity Theory : Volume 33, Issue 7 (23/07/2015)  
Author: Vlasov, M. N.
Volume: Vol. 33, Issue 7
Language: English
Subject: Science, Annales, Geophysicae
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Historic
Publication Date:
2015
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Vlasov, M. N., & Kelley, M. C. (2015). Eddy Diffusion Coefficients and Their Upper Limits Based on Application of the Similarity Theory : Volume 33, Issue 7 (23/07/2015). Retrieved from http://worldlibrary.in/


Description
Description: School of Electrical and Computer Engineering, Cornell University, Ithaca, New York, USA. 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.

Summary
Eddy diffusion coefficients and their upper limits based on application of the similarity theory

Excerpt
Bishop, R. L., Larsen, M. F., Hecht, J. H., Liu, A. Z., and Gardner, C. S.: TOMEX: Mesospheric and lower thermospheric diffusivity and instability layers, J. Geophys. Res., 109, D02S03, doi:10.1029/2002JD003079, 2004.; Hecht, J. H., Liu, A. Z., Walterscheid, R. L., Roble, R. G., Larsen, M. F., and Clemmons, J. H.: Airglow emissions and oxygen mixing ratios from the photometer experiment on the Turbulent Oxygen Mixing Experiment (TOMEX), J. Geophys. Res., 109, D02S05, 2004.; Heisenberg, W.: Zur statistischen Theorie der Turbulenz, Z. Phys., 124, 628–657, 1948.; Banks, P. M. and Kockarts, G.: Aeronomy, Academic Press, New York, USA, 1973.; Chandra, S.: Energetics and thermal structure of the middle atmosphere, Planet. Space Sci., 28, 585–593, 1980.; Gordiets, B. F., Kulikov, Y. N., Markov, M. N., and Marov, M. Y.: Numerical modeling of the thermospheric heat budget, J. Geophys. Res., 87, 4504–4514, 1982.; Kelley, M. C., Kruschwitz, C. A., Gardner, C. S., Drummond, J. D., and Kane, T. J.: Mesospheric turbulence measurements from persistent Leonid meteor train observations, J. Geophys. Res., 108, 8454, doi:10.1029/2002JD002392, 2003.; Kelley, M. C., Seyler, C. E., and Larsen, M. F.: Two-dimensional turbulence, space shuttle plume transport in the thermosphere, and a possible relation to the Great Siberian Impact Event, Geophys. Res. Lett., 36, L14103, doi:10.1029/2009GL038362, 2009.; Larsen, M. F.: Winds and shears in the mesosphere and lower thermosphere: Results from four decades of chemical release wind measurements, J. Geophys. Res., 107, 1215, doi:1029/2001JA000218, 2002.; Lübken, F. J.: Seasonal variation of turbulent energy dissipation rates at high latitudes as determined by in situ measurements of neutral density fluctuations, J. Geophys. Res., 102, 13441–13456, 1997.; Lübken, F. J., Hillert, W., Lehmacher, G., and von Zahn, U.: Experiments revealing small impact of turbulence on the energy budget of the mesosphere and lower thermosphere, J. Geophys. Res., 98, 20369–20384, 1993.; Sasi, M. N. and Vijayan, L.: Turbulence characteristics in the tropical mesosphere as obtained by MST radar at Gadanki (13.5° N, 79.2° E), Ann. Geophys., 19, 1019–1025, doi:10.5194/angeo-19-1019-2001, 2001.; Shimazaki, T.: Effective eddy diffusion coefficient and atmospheric composition in the lower thermosphere, J. Atmos. Terr. Phys., 33, 1383–1401, 1971.; Szewczyk, A., Strelnikov, B., Rapp, M., Strelnikova, I., Baumgarten, G., Kaifler, N., Dunker, T., and Hoppe, U.-P.: Simultaneous observations of a Mesospheric Inversion Layer and turbulence during the ECOMA-2010 rocket campaign, Ann. Geophys., 31, 775–785, 2013.; Taylor, G. I.: Diffusion by continuous movements, Proc. London Math. Soc., 20, 196–212, 1921.; Vlasov, M. N. and Kelley, M. C.: Criterion for analyzing experimental data on eddy diffusion coefficients, Ann. Geophys., 32, 581–588, doi:10.5194/angeo-32-581-2014, 2014.; Weinstock, J.: Vertical turbulent diffusion in a stably stratified fluid, J. Atmos. Sci., 35, 1022–1027, 1978.; Weinstock, J.: Energy dissipation rates of turbulence in the stable free atmosphere, J. Atmos. Sci., 38, 880–883, 1981.

 

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