MODELING OF THE NON-TURBULENT SURFACE LAYER ELECTRODYNAMIC STRUCTURE
Abstract
The article presents an electrodynamic model of the atmospheric surface layer caused by
the action of the electrode effect near the earth's surface, and an analysis of its equations by methods
of similarity theory. Mathematical models of the surface layer electrical state in the approximations
of the classical and turbulent electrode effect are considered separately. In the mathematical
formulation of modeling problems, a number of well-founded physical assumptions were created
that made it possible to obtain analytical solutions to the equations. Analytical formulas have
been obtained for calculating the profiles of aeroion concentrations, the density of the space electric
charge and the electric field in the electrode layer. As a result of mathematical modeling, the
dependences of the electrical characteristics distribution in the surface layer on the values of the
electric field, the degree of air ionization and aerosol pollution of the atmosphere are investigated.
It is shown that the ratio of the electric field values on the earth's surface and at the upper boundary
of the electrode layer is almost constant. The increasing of the electric field, the rate of air
ionization and the presence of sufficient concentration aerosol particles leads to a decrease in the
thickness of the electrode layer and, as a consequence, the scale of distribution of its parameters.
An amplification in the degree of ionization increases, and an increase in the concentration of
aerosol particles in the atmosphere decreases the values of the electric charge density in the surface
layer. Theoretical calculations are in good agreement with experimental data and the results
of numerical modeling of the surface layer electrical structure. The analytical formulas obtained
in the work for calculating the electrical characteristics of the surface layer and the results of
calculations can be useful in solving a number of applied problems of geophysics, in particular for
monitoring the electrical state of the atmosphere.
References
(spravochnye dannye, modeli) [Atmosphere. Reference book (reference data, models)]. Leningrad:
Gidrometeoizdat, 1991, pp. 394-408.
2. Kupovykh G.V., Morozov V.N., Shvarts Ya.M. Teoriya elektrodnogo effekta v atmosphere
[Theory of the electrode effect in the atmosphere]. Taganrog: Izd-vo TRTU, 1998, 123 p.
3. Kupovykh G.V. Elektrodinamicheskie protsessy v prizemnom sloe atmosfery [Electrodynamic
processes in the surface layer of the atmosphere]. Taganrog: Izd-vo TTI YuFU, 2009, 114 p.
4. Svidel'skiy S.S., Litvinova V.S., Kupovykh G.V., Klovo A.G. Formirovanie struktury atmosfernogo
elektrodnogo sloya [Formation of the structure of the atmospheric electrode layer], Izvestiya YuFU.
Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2020, No. 5, pp. 130-141.
5. Hoppel W.A. Theory of the electrode effect, Journal Atmospheric and Terrestrial Physics,
1967, Vol. 29, No. 6, pp. 709-721.
6. Kupovykh G.V., Morozov V.N. Klassicheskiy (neturbulentnyy) elektrodnyy effekt v prizemnom
sloe [Classical (non-turbulent) electrode effect in the surface layer], Izvestiya vysshikh
uchebnykh zavedeniy. Severo-Kavkazskiy region. Estestvennye nauki [Izvestia of higher educational
institutions. North Caucasus region. Natural sciences], 2003, No. 2, pp. 43-46.
7. Kupovykh G.V., Klovo A.G., Timoshenko D.V., Svidel'skiy S.S. Priblizhennoe analiticheskoe
reshenie zadachi ob elektrodinamicheskom sostoyanii prizemnoy atmosfery v usloviyakh
aerozol'nogo zagryazneniya [Approximate analytical solution to the problem of the
electrodynamic state of the surface atmosphere in aerosol pollution conditions], Izvestiya vysshikh
uchebnykh zavedeniy. Severo-Kavkazskiy region. Estestvennye nauki [Izvestia of higher educational
institutions. North Caucasus region. Natural sciences], 2018, No. 2, pp. 84-89.
8. Redin A.A., Klovo A.G., Kupovykh G.V. Elektrodinamicheskaya model' atmosfernogo prizemnogo
sloya [Electrodynamic model of the atmospheric surface layer], Izvestiya YuFU.
Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2009, No. 8, pp. 93-106.
9. Hoppel W.A. Electrode effect: comparison of the theory and measurement, In: Planetary Electrodynamics,
2, S.C. Coroniti and J. Hughes; ed.: Gordon and Breach Science Publishers,
New York, 1969, pp. 167-181.
10. Kupovykh G.V. Elektrichestvo prizemnogo sloya [Electricity of the surface layer], Izvestiya
vuzov. Severo-Kavkazskiy region. Estestvennye nauki [Izvestia of higher educational institutions,
Sev.-Kav. reg., Estest. Sciences], 1995, No. 4, pp. 32-34.
11. Redin A.A., Klovo A.G., Kupovykh G.V., Morozov V.N. Generatsiya ob"emnogo zaryada vblizi
poverkhnosti zemli s uchetom vzaimodeystviya aerozol'nykh chastits s aeroionami [Generation
of volumetric charge near the earth's surface, taking into account the interaction of aerosol particles
with aeroions], Izvestiya vysshikh uchebnykh zavedeniy. Severo-Kavkazskiy region.
Estestvennye nauki. Spetsvypusk. Fizika atmosfery [Izvestia of higher educational institutions.
North Caucasus region. Natural sciences. Special issue. Atmospheric physics], 2010, pp. 81-85.
12. Redin A.A., Klovo A.G., Kupovykh G.V. Matematicheskoe modelirovanie elektrodinamicheskoy
struktury prizemnogo sloya atmosfery v usloviyakh aerozol'nogo zagryazneniya [Mathematical
modeling of the electrodynamic structure of the surface layer of the atmosphere under aerosol pollution
conditions], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences],
2009, No. 7 (96), pp. 192-200.
13. Kupovykh G.V., Boldyrev A.S., Litvinova I.S, Marchenko A.G. O svyazi elektricheskogo polya s
ob"emnym zaryadom v prizemnom sloe atmosfery [On the connection of an electric field with a
volumetric charge in the surface layer of the atmosphere], Izvestiya vysshikh uchebnykh zavedeniy.
Severo-Kavkazskiy region. Estestvennye nauki. Prilozhenie № 3 [Izvestia of higher educational institutions.
North Caucasus region. Natural sciences. Appendix No. 3], 2003, pp. 42-45.
14. Hoppel W.A., Frick G.M. Ion-Aerosol Attachment Coefficients and the Steady-State Charge
Distribution on Aerosols in a Bipolar Ion Environment, Aerosol Science and Technology,
1986, 5:1, pp. 1-21.
15. Hoppel W.A. Ionaerosol attachment,ion depletion and charge distribution on aerosols,
J. Geoph. Res., 1985, Vol. 90, No. D4, pp. 5917-5923.
16. Kupovykh G., Redin A., Boldyreff A. Modeling of ionization-recombination processes in the
atmospheric surface layer, Journal of Electrostatics 71. Elsevier B.V., 2013, pp. 305-311.
17. Kupovykh G.V., Timoshenko D.V., Klovo A. G., Kudrinskaya T.V. Electrodynamic processes
models in atmospheric surface layer, IOP Conference Series: Materials Science and Engineering,
2019, Vol. 698 044034, 8 p.
18. Kudrinskaya T.V., Kupovykh G.V., Redin A.A. Issledovaniya ionizatsionnogo sostoyaniya
prizemnogo sloya atmosfery v raznykh geofizicheskikh usloviyakh [Studies of the ionization
state of the surface layer of the atmosphere in different geophysical conditions], Meteorologiya
i gidrologiya [Meteorology and hydrology], 2018, No. 4, pp. 77-85.
19. Shuleykin V.N., Shchukin G.G., Kupovykh G.V. Razvitie metodov i sredstv prikladnoy geofiziki
– atmosferno-elektricheskiy monitoring geologicheskikh neodnorodnostey i zon
geodinamicheskikh protsessov [Development of methods and means of applied geophysics -
atmospheric and electrical monitoring of geological heterogeneities and zones of geodynamic
processes]. Saint Petersburg: RGGMU, 2015, 206 p.
20. Kupovykh G.V., Kudrinskaya T.V., Grivtsov V.V. The atmosphere electrical characteristics’
monitoring as an element of technosphere safety, IOP Conference Series: Materials Science
and Engineering, 2020. 913 052041, 6 p.
