Influence of Vibration on the Onset of Convection in Second Grade Fluid

Influence of Vibration on the Onset of Convection in Second Grade Fluid Full article

Journal

Computational Mathematics and Mathematical Physics
ISSN: 0965-5425

Output data

Year: 2025, Volume: 65, Number: 5, Pages: 1140-1147 Pages count : 8 DOI: 10.1134/S0965542525700356

Tags

second grade fluid, relaxation viscosity, vertical vibrations

Authors

Pukhnachev V.V. ¹ , Frolovskaya O.A. ¹

Affiliations

1	Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences

The problem of convective stability of a second grade incompressible fluid in a horizontal layer heated from below is considered. The fluid is subjected to vertical or horizontal vibrations. A state of relative equilibrium is possible in this situation. The case of high-frequency vibrations is considered first. Specifically, the averaging method is used to formulate a spectral problem for finding the critical Rayleigh number; this problem is similar to the one arising in the classical problem of convective stability of a Newtonian fluid. It is shown that the critical Rayleigh number increases insignificantly when relaxation terms are taken into account. Similar results are obtained by analyzing the stability of relative equilibrium in the case of finite-frequency vertical vibrations.

Pukhnachev V.V. , Frolovskaya O.A.
Influence of Vibration on the Onset of Convection in Second Grade Fluid
Computational Mathematics and Mathematical Physics. 2025. V.65. N5. P.1140-1147. DOI: 10.1134/S0965542525700356

Пухначев В.В. , Фроловская О.А.
Влияние вибраций на возникновение конвекции в жидкости второго порядка
Журнал вычислительной математики и математической физики. 2025. Т.65. №5. С.807-814. DOI: 10.31857/S0044466925050166

Submitted:	Dec 11, 2024
Accepted:	Feb 25, 2025

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