BIFURCATIONS IN THE PROBLEM OF THERMAL CONVECTION OF VISCOELASTIC FLUID IN A CLOSED CAVITY WITH FREE BOUNDARIES HEATED FROM BELOW

Cite this article as:

Lyubimov D. V., Kovalevskaya К. V., Lyubimova Т. P. BIFURCATIONS IN THE PROBLEM OF THERMAL CONVECTION OF VISCOELASTIC FLUID IN A CLOSED CAVITY WITH FREE BOUNDARIES HEATED FROM BELOW. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 3, pp. 16-25. DOI: https://doi.org/10.18500/0869-6632-2011-19-3-16-25

Bifurcations in the problem of thermal convection of viscoelastic fluid in a square cavity with free boundaries heated from below are studied. General Odroyd model is used for the description of rheological behaviour of the fluid. In the frame of weakly­nonlinear analysis explicit formula is obtained for the boundary separating the rheological parameter space into domains with different type of bifurcations (super­ and subcritical).

Authors: 
Lyubimov D. V., Федеральное государственное бюджетное образовательное учреждение высшего профессионального образования «Пермский государственный национальный исследовательский университет» , 614990 Пермь, ул. Букирева, 15 , lyubimov@psu.ru
Kovalevskaya К. V., Институт механики сплошных сред Уральского отделения РАН (ИМСС УрО РАН), 614013 Пермь, ул. Академика Королева, 1 , k_kovalevskaya@mail.ru
Lyubimova Т. P., Институт механики сплошных сред Уральского отделения РАН (ИМСС УрО РАН), 614013 Пермь, ул. Академика Королева, 1 , lubimova@psu.ru
Key words: 
Viscoelastic fluid, convection, closed cavity, weakly­nonlinear analysis, super­critical bifurcation, subcritical bifurcation.
DOI: 
10.18500/0869-6632-2011-19-3-16-25
Literature

1. Vest C.V., Arpaci V.S. Overstability of a viscoelastic fluid layer heated from below // J. Fluid Mech. 1969. Vol. 36. Part 3. P. 613.

2. Takashima M. Thermal instability in viscoelastic fluid layer. I // Journal of the Physical Society of Japan. 1972. Vol. 33, No 2. P. 511.

3. Rosenblat S. Thermal convection in a viscoelastic liquid // J. Non-Newtonian Fluid Mech. 1986. Vol. 21. P. 201.

4. Park H.M., Lee H.S. Nonlinear hydrodynamic stability of viscoelastic fluids heated from below // J. Non-Newtonian Fluid Mech. 1995. Vol. 60. I. 1. P. 1.

5. Ковалевская К.В., Любимова Т.П. Возникновение и нелинейные режимы конвекции упруговязкой жидкости в замкнутой полости при подогреве снизу // Изв. РАН. МЖГ. 2012 (принято в печать).

6. Крапивина Е.Н., Любимова Т.П. Нелинейные режимы конвекции упруго-вязкой жидкости в замкнутой полости, подогреваемой снизу // Изв. РАН. МЖГ. 2000. No 4. С. 5.

7. Астарита Дж., Маруччи Дж. Основы гидродинамики неньютоновских жидкостей. М.: Мир, 1978.

Heading: 
Bifurcations in Dynamical Systems
Status: 
одобрено к публикации
Short Text (PDF): 
a2011no3p016.pdf
Full Text (PDF): 
2011no3p016.pdf

BibTeX

@article{Любимов -IzvVUZ_AND-19-3-16,
author = {D. V. Lyubimov and К. V. Kovalevskaya and Т. P. Lyubimova},
title = {BIFURCATIONS IN THE PROBLEM OF THERMAL CONVECTION OF VISCOELASTIC FLUID IN A CLOSED CAVITY WITH FREE BOUNDARIES HEATED FROM BELOW},
year = {2011},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {19},number = {3},
url = {https://old-andjournal.sgu.ru/en/articles/bifurcations-in-the-problem-of-thermal-convection-of-viscoelastic-fluid-in-closed-cavity},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2011-19-3-16-25},pages = {16--25},issn = {0869-6632},
keywords = {Viscoelastic fluid,convection,closed cavity,weakly­nonlinear analysis,super­critical bifurcation,subcritical bifurcation.},
abstract = {Bifurcations in the problem of thermal convection of viscoelastic fluid in a square cavity with free boundaries heated from below are studied. General Odroyd model is used for the description of rheological behaviour of the fluid. In the frame of weakly­nonlinear analysis explicit formula is obtained for the boundary separating the rheological parameter space into domains with different type of bifurcations (super­ and subcritical). }}