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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 3, Pages 462–475 (Mi zvmmf11048)  

Stochastic model of heat transfer in the atmospheric surface layer

V. G. Zadorozhniyab, V. S. Nozhkinb, M. Y. Semenovabc, I. I. Ul'shinb

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

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.


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


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:3, 459–471

Bibliographic databases:

UDC: 519.776
Received: 10.02.2019
Revised: 10.02.2019
Accepted:18.11.2019

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

Citation in format AMSBIB
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\by V.~G.~Zadorozhniy, V.~S.~Nozhkin, M.~Y.~Semenov, I.~I.~Ul'shin
\paper Stochastic model of heat transfer in the atmospheric surface layer
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2020
\vol 60
\issue 3
\pages 462--475
\mathnet{http://mi.mathnet.ru/zvmmf11048}
\crossref{https://doi.org/10.31857/S0044466920030175}
\elib{https://elibrary.ru/item.asp?id=42445969}
\transl
\jour Comput. Math. Math. Phys.
\yr 2020
\vol 60
\issue 3
\pages 459--471
\crossref{https://doi.org/10.1134/S0965542520030173}
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