Skip to main content
Top
Published in: Fluid Dynamics 8/2022

01-12-2022

On Estimation of the Contribution of Secondary Vortex Structures to the Transport of Aerosols in the Atmospheric Boundary Layer

Authors: M. A. Davydova, O. G. Chkhetiani, N. T. Levashova, A. L. Nechaeva

Published in: Fluid Dynamics | Issue 8/2022

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, we consider two reasonable approaches to the problem of numerical simulation of the concentration distribution of a finely dispersed aerosol in spiral vortex structures (rolls) at the atmospheric boundary layer in order to estimate the contribution of vortex structures to the transport of aerosols through the boundary layer. Using the methods of perturbation theory, an approximate solution of a stationary spatially periodic singularly perturbed problem of the reaction–diffusion–advection type, which models the distribution of an aerosol in vortices, is obtained, the residual term is estimated, and a method for numerically solving the zero-approximation problem is proposed. As an alternative approach to the problem of numerical modeling of an aerosol-concentration field in rolls, implementation of the method of evolutionary factorization is considered. Using model data, an estimate of the amount of an aerosol carried by vortex structures is obtained.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Lilly, D.K., On the stability of Ekman boundary flow, J. Atmos. Sci., 1966, vol. 23, no. 5, pp. 481–494.ADSCrossRef Lilly, D.K., On the stability of Ekman boundary flow, J. Atmos. Sci., 1966, vol. 23, no. 5, pp. 481–494.ADSCrossRef
2.
go back to reference Ponomarev, V.M., Khapaev, A.A., and Chkhetiani, O.G., Role of helicity in the formation of secondary structures in the Ekman boundary layer, Izv., Atmos. Ocean. Phys., 2003, vol. 39, no. 4, pp. 391–400.MathSciNet Ponomarev, V.M., Khapaev, A.A., and Chkhetiani, O.G., Role of helicity in the formation of secondary structures in the Ekman boundary layer, Izv., Atmos. Ocean. Phys., 2003, vol. 39, no. 4, pp. 391–400.MathSciNet
3.
go back to reference Thompson, T.W., Liu, W.T., and Weissman, D.E., Synthetic aperture radar observation of the ocean roughess from rolls in an unstable marine boundary layer, J. Geophys. Res., 1983, vol. 10, pp. 172–175. Thompson, T.W., Liu, W.T., and Weissman, D.E., Synthetic aperture radar observation of the ocean roughess from rolls in an unstable marine boundary layer, J. Geophys. Res., 1983, vol. 10, pp. 172–175.
4.
go back to reference Mourad, P.D. and Walter, B.A., Sar streaks vs cloud streets: viewing a cold air outbreak using satelite-based SAR and AVHRR imagery, J. Geophys. Res., 1996, vol. 101, pp. 16391–16400.ADSCrossRef Mourad, P.D. and Walter, B.A., Sar streaks vs cloud streets: viewing a cold air outbreak using satelite-based SAR and AVHRR imagery, J. Geophys. Res., 1996, vol. 101, pp. 16391–16400.ADSCrossRef
5.
go back to reference Atkinson, B.W. and Wu Zhang, J., Mesoscale shallow convection in the atmosphere, Rev. Geophys., 1996, vol. 34, no. 4, pp. 403–431.ADSCrossRef Atkinson, B.W. and Wu Zhang, J., Mesoscale shallow convection in the atmosphere, Rev. Geophys., 1996, vol. 34, no. 4, pp. 403–431.ADSCrossRef
6.
go back to reference Brummer, B., Structure, dynamics and energetics of boundary layer from Kontur aircraft observations, Beitr. Phys. Atmos., 1985, vol. 58, pp. 237–254. Brummer, B., Structure, dynamics and energetics of boundary layer from Kontur aircraft observations, Beitr. Phys. Atmos., 1985, vol. 58, pp. 237–254.
7.
go back to reference Chou, S.-H. and Ferguson, M.P., Heat fluxes and roll circulation over the western gulf stream during an intense cold-air outbreak, Boundary Layer Meteorol., 1991, vol. 55, no. 3, pp. 255–281.ADSCrossRef Chou, S.-H. and Ferguson, M.P., Heat fluxes and roll circulation over the western gulf stream during an intense cold-air outbreak, Boundary Layer Meteorol., 1991, vol. 55, no. 3, pp. 255–281.ADSCrossRef
8.
go back to reference Gerling, T.W., Structure of the surface wind fields from Seasat SAR, J. Geophys. Res., 1986, vol. 91, pp. 2308–2320.ADSCrossRef Gerling, T.W., Structure of the surface wind fields from Seasat SAR, J. Geophys. Res., 1986, vol. 91, pp. 2308–2320.ADSCrossRef
9.
go back to reference Alpers, W. and Brummer, B., Atmospheric boundary layer rolls observed by the synthetic aperture radar aboard the ERS-1 satellite, J. Geophys. Res., 1994, vol. 99, pp. 12613–12621.ADSCrossRef Alpers, W. and Brummer, B., Atmospheric boundary layer rolls observed by the synthetic aperture radar aboard the ERS-1 satellite, J. Geophys. Res., 1994, vol. 99, pp. 12613–12621.ADSCrossRef
10.
go back to reference Golitsyn, G.S., Granberg, I.G., Andronova, A.V., Ponomarev, V.M., Zilitinkevich, S.S., Smirnov, V.V., and Yablokov, M.Yu., Investigation of boundary layer fine structure in arid regions: injection of fine dust into the atmosphere, Water, Air Soil Pollut.: Focus, 2003, vol. 3, pp. 245–257.CrossRef Golitsyn, G.S., Granberg, I.G., Andronova, A.V., Ponomarev, V.M., Zilitinkevich, S.S., Smirnov, V.V., and Yablokov, M.Yu., Investigation of boundary layer fine structure in arid regions: injection of fine dust into the atmosphere, Water, Air Soil Pollut.: Focus, 2003, vol. 3, pp. 245–257.CrossRef
11.
go back to reference Vazaeva, N.V., Chkhetiani, O.G., Shestakova, L.V., and Maksimenkov, L.O., Nonlinear development of the Ekman layer structures, Vychisl. Mekh. Sploshnykh Sred, 2017, vol. 10, no. 2, pp. 197–211. Vazaeva, N.V., Chkhetiani, O.G., Shestakova, L.V., and Maksimenkov, L.O., Nonlinear development of the Ekman layer structures, Vychisl. Mekh. Sploshnykh Sred, 2017, vol. 10, no. 2, pp. 197–211.
12.
go back to reference LeMone, M.A., The structure and dynamics of horizontal roll vortices in the planetary boundary layer, J. Atmos. Sci., 1973, vol. 30, pp. 1077–1091.ADSCrossRef LeMone, M.A., The structure and dynamics of horizontal roll vortices in the planetary boundary layer, J. Atmos. Sci., 1973, vol. 30, pp. 1077–1091.ADSCrossRef
13.
go back to reference Lampilahti, J., Manninen, H.E., Leino, K., et al., Roll vortices induce new particle formation bursts in the planetary boundary layer, Atmos. Chem. Phys., 2020, vol. 20, no. 20, pp. 11841–11854.ADSCrossRef Lampilahti, J., Manninen, H.E., Leino, K., et al., Roll vortices induce new particle formation bursts in the planetary boundary layer, Atmos. Chem. Phys., 2020, vol. 20, no. 20, pp. 11841–11854.ADSCrossRef
14.
go back to reference Zedel, L. and Farmer, D.M., Organised structures in subsurface bubble clouds: Langmuir circulation in the open ocean, J. Geophys. Res., 1991, vol. 96, pp. 8889–8900.ADSCrossRef Zedel, L. and Farmer, D.M., Organised structures in subsurface bubble clouds: Langmuir circulation in the open ocean, J. Geophys. Res., 1991, vol. 96, pp. 8889–8900.ADSCrossRef
15.
go back to reference Ivlev, L.S. and Dovgalyuk, Yu.A., Fizika atmosfernykh aerozol’nykh sistem (Physics of Atmospheric Aerosol Systems), St. Petersburg: Saint Petersburg Institute of Chemistry, 1999. Ivlev, L.S. and Dovgalyuk, Yu.A., Fizika atmosfernykh aerozol’nykh sistem (Physics of Atmospheric Aerosol Systems), St. Petersburg: Saint Petersburg Institute of Chemistry, 1999.
16.
go back to reference Joint MSC-W&CCC&CEIP Rep. Transboundary particulate matter, photo-oxidants, acidifying and eutrophying components. https://emep.int/publ/reports/2019/EMEP\_Status\_Report\_1\_2019.pdf. Joint MSC-W&CCC&CEIP Rep. Transboundary particulate matter, photo-oxidants, acidifying and eutrophying components. https://​emep.​int/​publ/​reports/​2019/​EMEP\_Status\_Report\_1\_2019.pdf.
17.
go back to reference Marchuk, G.I., Matheematical Models in Environmental Problems, Amsterdam: Elsevier, 1986. Marchuk, G.I., Matheematical Models in Environmental Problems, Amsterdam: Elsevier, 1986.
18.
go back to reference Berlyand, M.E., Prediction and Regulation of Air Pollution, Netherlands: Springer, 1991.CrossRef Berlyand, M.E., Prediction and Regulation of Air Pollution, Netherlands: Springer, 1991.CrossRef
19.
go back to reference Ponomarev, V.M., Chkhetiani, O.G., and Shestakova, L.V., Nonlinear dynamics of large-scale vortex structures in a turbulent Ekman layer, Fluid Dyn., 2007, vol. 42, no. 2, pp. 571–580.ADSMathSciNetCrossRefMATH Ponomarev, V.M., Chkhetiani, O.G., and Shestakova, L.V., Nonlinear dynamics of large-scale vortex structures in a turbulent Ekman layer, Fluid Dyn., 2007, vol. 42, no. 2, pp. 571–580.ADSMathSciNetCrossRefMATH
20.
go back to reference Nefedov, N.N., The method of differential inequalities for some singularly perturbed partial differential equations, Differ. Equations, 1995, vol. 31, no. 4, pp. 668–671.MathSciNetMATH Nefedov, N.N., The method of differential inequalities for some singularly perturbed partial differential equations, Differ. Equations, 1995, vol. 31, no. 4, pp. 668–671.MathSciNetMATH
21.
go back to reference Ladyzhenskaya, O.A. and Ural’tseva, N.N., Linear and Quasilinear Elliptic Equations, New York: Academic, 1968.MATH Ladyzhenskaya, O.A. and Ural’tseva, N.N., Linear and Quasilinear Elliptic Equations, New York: Academic, 1968.MATH
22.
go back to reference Miranda, C., Equazioni alle derivate parziali di tipo ellittico, Berlin: Springer, 1955.MATH Miranda, C., Equazioni alle derivate parziali di tipo ellittico, Berlin: Springer, 1955.MATH
23.
go back to reference Friedman, A., Partial Differential Equations of Parabolic Type, Englewood Cliffs, N.J.: Prentice-Hall, 1964.MATH Friedman, A., Partial Differential Equations of Parabolic Type, Englewood Cliffs, N.J.: Prentice-Hall, 1964.MATH
24.
go back to reference Davydova, M.A., Elanskii, N.F., Zakharova, S.A., and Postylyakov, O.V., Application of a numerical-asymptotic approach to the problem of restoring the parameters of a local stationary source of anthropogenic pollution, Dokl. Math., 2021, vol. 103, no. 1, pp. 26–31.MathSciNetCrossRefMATH Davydova, M.A., Elanskii, N.F., Zakharova, S.A., and Postylyakov, O.V., Application of a numerical-asymptotic approach to the problem of restoring the parameters of a local stationary source of anthropogenic pollution, Dokl. Math., 2021, vol. 103, no. 1, pp. 26–31.MathSciNetCrossRefMATH
25.
go back to reference Zakharova, S.A., Davydova, M.A., and Lukyanenko, D.V., Use of asymptotic analysis for solving the inverse problem of source parameters determination of nitrogen oxide emission in the atmosphere, Inverse Prob. Sci. Eng., 2021, vol. 29, no. 3, pp. 365–377.MathSciNetCrossRefMATH Zakharova, S.A., Davydova, M.A., and Lukyanenko, D.V., Use of asymptotic analysis for solving the inverse problem of source parameters determination of nitrogen oxide emission in the atmosphere, Inverse Prob. Sci. Eng., 2021, vol. 29, no. 3, pp. 365–377.MathSciNetCrossRefMATH
26.
go back to reference Davydova, M.A., Elanskii, N.F., and Zakharova, S.A., A new approach to the problem of reconstructing the vertical turbulent diffusion coefficient in the atmospheric boundary layer, Dokl. Earth Sci., 2020, vol. 490, no. 2, pp. 92–96.ADSCrossRef Davydova, M.A., Elanskii, N.F., and Zakharova, S.A., A new approach to the problem of reconstructing the vertical turbulent diffusion coefficient in the atmospheric boundary layer, Dokl. Earth Sci., 2020, vol. 490, no. 2, pp. 92–96.ADSCrossRef
27.
go back to reference Davydova, M.A. and Zakharova, S.A., Multidimensional thermal structures in the singularly perturbed stationary models of heat and mass transfer with a nonlinear thermal diffusion coefficient, J. Comput. Appl. Math., 2022, vol. 400, p. 113731. Davydova, M.A. and Zakharova, S.A., Multidimensional thermal structures in the singularly perturbed stationary models of heat and mass transfer with a nonlinear thermal diffusion coefficient, J. Comput. Appl. Math., 2022, vol. 400, p. 113731.
28.
go back to reference Lukyanenko, D.V., Borzunov, A.A., and Shishlenin, M.A., Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front, Commun. Nonlin. Sci. Numer. Simul., 2021, vol. 99, p. 105824. Lukyanenko, D.V., Borzunov, A.A., and Shishlenin, M.A., Solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection type with data on the position of a reaction front, Commun. Nonlin. Sci. Numer. Simul., 2021, vol. 99, p. 105824.
29.
go back to reference Argun, R., Gorbachev, A., Levashova, N., and Lukyanenko, D., Inverse problem for an equation of the reaction-diffusion-advection type with data on the position of a reaction front: features of the solution in the case of a nonlinear integral equation in a reduced statement, Mathematics, 2021, vol. 9, no. 18, p. 2342.CrossRef Argun, R., Gorbachev, A., Levashova, N., and Lukyanenko, D., Inverse problem for an equation of the reaction-diffusion-advection type with data on the position of a reaction front: features of the solution in the case of a nonlinear integral equation in a reduced statement, Mathematics, 2021, vol. 9, no. 18, p. 2342.CrossRef
30.
go back to reference Lukyanenko, D., Yeleskina, T., Prigorniy, I., Isaev, T., Borzunov, A., and Shishlenin, M., Inverse problem of recovering the initial condition for a nonlinear equation of the reaction-diffusion-advection type by data given on the position of a reaction front with a time delay, Mathematics, 2021, vol. 9, no. 4, p. 342.CrossRef Lukyanenko, D., Yeleskina, T., Prigorniy, I., Isaev, T., Borzunov, A., and Shishlenin, M., Inverse problem of recovering the initial condition for a nonlinear equation of the reaction-diffusion-advection type by data given on the position of a reaction front with a time delay, Mathematics, 2021, vol. 9, no. 4, p. 342.CrossRef
31.
go back to reference Levashova, N., Gorbachev, A., Argun, R., and Lukyanenko, D., The problem of the non-uniqueness of the solution to the inverse problem of recovering the symmetric states of a bistable medium with data on the position of an autowave front, Symmetry, 2021, vol. 13, no. 5, p. 860.ADSCrossRef Levashova, N., Gorbachev, A., Argun, R., and Lukyanenko, D., The problem of the non-uniqueness of the solution to the inverse problem of recovering the symmetric states of a bistable medium with data on the position of an autowave front, Symmetry, 2021, vol. 13, no. 5, p. 860.ADSCrossRef
32.
go back to reference Lukyanenko, D.V., Prigorniy, I.V., and Shishlenin, M.A., Some features of solving an inverse backward problem for a generalized burgers’ equation, J. Inverse Ill-Posed Probl., 2020, vol. 28, no. 5, pp. 641–649.MathSciNetCrossRefMATH Lukyanenko, D.V., Prigorniy, I.V., and Shishlenin, M.A., Some features of solving an inverse backward problem for a generalized burgers’ equation, J. Inverse Ill-Posed Probl., 2020, vol. 28, no. 5, pp. 641–649.MathSciNetCrossRefMATH
33.
go back to reference Ponomarev, V.M., Chkhetiani, O.G., and Shestakova, L.V., Numerical modeling of developed horizontal circulation in the atmospheric boundary layer, Vychisl. Mekh. Sploshnykh Sred, 2009, vol. 2, no. 1, pp. 68–80. Ponomarev, V.M., Chkhetiani, O.G., and Shestakova, L.V., Numerical modeling of developed horizontal circulation in the atmospheric boundary layer, Vychisl. Mekh. Sploshnykh Sred, 2009, vol. 2, no. 1, pp. 68–80.
34.
go back to reference Vazaeva, N.V., Chkhetiani, O.G., and Maksimenkov, L.O., Organized roll circulation and transport of mineral aerosols in the atmospheric boundary layer, Izv., Atmos. Ocean. Phys., 2019, vol. 55, no. 2, pp. 17–31.CrossRef Vazaeva, N.V., Chkhetiani, O.G., and Maksimenkov, L.O., Organized roll circulation and transport of mineral aerosols in the atmospheric boundary layer, Izv., Atmos. Ocean. Phys., 2019, vol. 55, no. 2, pp. 17–31.CrossRef
35.
go back to reference Mourad, P.D. and Brown, R.A., On multiscale large eddy states in weakly stratified boundary layers, J. Atmos. Sci., 1990, vol. 47, pp. 414–438.ADSMathSciNetCrossRef Mourad, P.D. and Brown, R.A., On multiscale large eddy states in weakly stratified boundary layers, J. Atmos. Sci., 1990, vol. 47, pp. 414–438.ADSMathSciNetCrossRef
36.
go back to reference Chkhetiani, O.G. and Vazaeva, N.V., On the algebraic perturbations in atmospheric boundary layer, Izv., Atmos. Ocean. Phys., 2019, vol. 55, no. 5, pp. 432–446.CrossRef Chkhetiani, O.G. and Vazaeva, N.V., On the algebraic perturbations in atmospheric boundary layer, Izv., Atmos. Ocean. Phys., 2019, vol. 55, no. 5, pp. 432–446.CrossRef
37.
go back to reference Kalitkin, N.N. and Koryakin, P.V., Chislennye metody: v 2 kn (Numerical Methods. In 2 Books), book 2: Metody matematicheskoi fiziki (Methods of Mathematical Physics), Moscow: ITs Akademiya, 2013. Kalitkin, N.N. and Koryakin, P.V., Chislennye metody: v 2 kn (Numerical Methods. In 2 Books), book 2: Metody matematicheskoi fiziki (Methods of Mathematical Physics), Moscow: ITs Akademiya, 2013.
38.
go back to reference Abramov, A.A. and Andreev, V.B., On the application of the sweep method for finding periodic solutions of differential and difference equations, Zh. Vychisl. Mat. Mat. Fiz., 1963, vol. 3, no. 2, pp. 377–381.MathSciNet Abramov, A.A. and Andreev, V.B., On the application of the sweep method for finding periodic solutions of differential and difference equations, Zh. Vychisl. Mat. Mat. Fiz., 1963, vol. 3, no. 2, pp. 377–381.MathSciNet
39.
go back to reference Kamke, E., Differential gleichungen Erster Ordnung fur Eine Gesuchte Funktion, Wiesbaden: Vieweg+Teubner Verlag, 1979. Kamke, E., Differential gleichungen Erster Ordnung fur Eine Gesuchte Funktion, Wiesbaden: Vieweg+Teubner Verlag, 1979.
40.
go back to reference Guermond, J.L., A finite element technique for solving first-order PDEs in Lp, SIAM J. Numer. Anal., 2004, vol. 42, no. 1, pp. 714–737.MathSciNetCrossRefMATH Guermond, J.L., A finite element technique for solving first-order PDEs in Lp, SIAM J. Numer. Anal., 2004, vol. 42, no. 1, pp. 714–737.MathSciNetCrossRefMATH
Metadata
Title
On Estimation of the Contribution of Secondary Vortex Structures to the Transport of Aerosols in the Atmospheric Boundary Layer
Authors
M. A. Davydova
O. G. Chkhetiani
N. T. Levashova
A. L. Nechaeva
Publication date
01-12-2022
Publisher
Pleiades Publishing
Published in
Fluid Dynamics / Issue 8/2022
Print ISSN: 0015-4628
Electronic ISSN: 1573-8507
DOI
https://doi.org/10.1134/S001546282208002X

Other articles of this Issue 8/2022

Fluid Dynamics 8/2022 Go to the issue

Premium Partners