Chaos, Solitons and Fractals, volume 78, pages 249-255
Analytic self-similar solutions of the Oberbeck–Boussinesq equations
2
Faculty of Science, Sapientia University, Libertătii sq. 1, Miercurea Ciuc, 530104, Romania
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Publication type: Journal Article
Publication date: 2015-09-01
Journal:
Chaos, Solitons and Fractals
scimago Q1
wos Q1
SJR: 1.349
CiteScore: 13.2
Impact factor: 5.3
ISSN: 09600779, 18732887
General Physics and Astronomy
Statistical and Nonlinear Physics
General Mathematics
Applied Mathematics
Abstract
In this article we will present pure two-dimensional analytic solutions for the coupled non-compressible Newtoniain Navier-Stokes --- with Boussinesq approximation --- and the heat conduction equation. The system was investigated from E.N. Lorenz half a century ago with Fourier series and pioneered the way to the paradigm of chaos. We present a novel analysis of the same system where the key idea is the two-dimensional generalization of the well-known self-similar Ansatz of Barenblatt which will be interpreted in a geometrical way. The results, the pressure, temperature and velocity fields are all analytic and can be expressed with the help of the error functions. The temperature field has a strongly damped oscillating behavior which is an interesting feature.
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Barna I., Mátyás L. Analytic self-similar solutions of the Oberbeck–Boussinesq equations // Chaos, Solitons and Fractals. 2015. Vol. 78. pp. 249-255.
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Barna I., Mátyás L. Analytic self-similar solutions of the Oberbeck–Boussinesq equations // Chaos, Solitons and Fractals. 2015. Vol. 78. pp. 249-255.
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TY - JOUR
DO - 10.1016/j.chaos.2015.08.002
UR - https://doi.org/10.1016/j.chaos.2015.08.002
TI - Analytic self-similar solutions of the Oberbeck–Boussinesq equations
T2 - Chaos, Solitons and Fractals
AU - Barna, I.F.
AU - Mátyás, László
PY - 2015
DA - 2015/09/01
PB - Elsevier
SP - 249-255
VL - 78
SN - 0960-0779
SN - 1873-2887
ER -
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@article{2015_Barna,
author = {I.F. Barna and László Mátyás},
title = {Analytic self-similar solutions of the Oberbeck–Boussinesq equations},
journal = {Chaos, Solitons and Fractals},
year = {2015},
volume = {78},
publisher = {Elsevier},
month = {sep},
url = {https://doi.org/10.1016/j.chaos.2015.08.002},
pages = {249--255},
doi = {10.1016/j.chaos.2015.08.002}
}