V. G. Zadorozhniy, V. S. Nozhkin, M. Y. Semenov, I. I. Ul'shin, “Stochastic model of heat transfer in the atmospheric surface layer”, Zh. Vychisl. Mat. Mat. Fiz., 60:3 (2020), 462–475; Comput. Math. Math. Phys., 60:3 (2020), 459

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 3, Pages 462–475
DOI: https://doi.org/10.31857/S0044466920030175 (Mi zvmmf11048)

This article is cited in 8 scientific papers (total in 8 papers)

Stochastic model of heat transfer in the atmospheric surface layer

V. G. Zadorozhniy^ab, V. S. Nozhkin^b, M. Y. Semenov^abc, I. I. Ul'shin^b

^a Voronezh State University, Voronezh, 394006 Russia
^b Zhukovsky and Gagarin Air Force Engineering Academy, Voronezh, 394064 Russia
^c Federal Research Center Geophysical Survey, Russian Academy of Sciences, Obninsk, 249035 Russia

Citations (8)

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DOI: https://doi.org/10.31857/S0044466920030175

Abstract: A new stochastic model of heat transfer in the atmospheric surface layer is proposed. The model is based on the experimentally confirmed fact that the horizontal wind velocity can be treated as a random process. Accordingly, the model is formalized using a differential equation with random coefficients. Explicit formulas for the expectation and the second moment function of the solution to the heat transfer equation with random coefficients are given. The error induced by replacing the random coefficient of the equation with its expectation is estimated. An example is given demonstrating the efficiency of the proposed approach in the case of a Gaussian distribution of the horizontal wind velocity, when the expectation and the second moment function can be determined within the framework of model representations.

Key words: heat transfer equation, variational derivative, random process, expectation, second moment function, characteristic functional.

Funding agency	Grant number
Russian Science Foundation	19-11-00197
The work by M.E. Semenov (see Sections 2, 3) was supported by the Russian Science Foundation, grant no. 19-11-00197.

Received: 10.02.2019
Revised: 10.02.2019
Accepted: 18.11.2019

English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 3, Pages 459–471
DOI: https://doi.org/10.1134/S0965542520030173

Bibliographic databases:

Document Type: Article

UDC: 519.776

Language: Russian

Citation: V. G. Zadorozhniy, V. S. Nozhkin, M. Y. Semenov, I. I. Ul'shin, “Stochastic model of heat transfer in the atmospheric surface layer”, Zh. Vychisl. Mat. Mat. Fiz., 60:3 (2020), 462–475; Comput. Math. Math. Phys., 60:3 (2020), 459–471

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Dmitrenko V A., “Prediction of Laminar-Turbulent Transition on Flat Plate on the Basis of Stochastic Theory of Turbulence and Equivalence of Measures”, Continuum Mech. Thermodyn., 34:2 (2022), 601–615
Artur V. Dmitrenko, “Theoretical calculation of the laminar–turbulent transition in the round tube on the basis of stochastic theory of turbulence and equivalence of measures”, Continuum Mech. Thermodyn., 34:6 (2022), 1375
R. Malek, Ch. Ziti, “A new numerical method to solve some PDE$_s$ in the unit ball and comparison with the finite element and the exact solution”, Int. J. Differ. Equat., 2021 (2021), 6696165
I E Kuznetcov, A A Kuznetcov, I O Baklanov, O V Strashko, “The probabilistic model of search and detection of ground objects using unmanned aerial vehicles in difficult weather conditions”, J. Phys.: Conf. Ser., 1745:1 (2021), 012048
S. V. Bogomolov, T. V. Zakharova, “Boltzmann equation without molecular chaos hypothesis”, Math. Models Comput. Simul., 13:5 (2021), 743–755
V. Nozhkin, M. Semenov, I. Ulshin, O. Sokolova, “A stochastic model of the moisture motion in the atmosphere: two-dimensional case”, 2020 Vi International Conference on Information Technology and Nanotechnology (IEEE Itnt-2020), ed. D. Kudryashov, IEEE, 2020

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