Thermal vibrational convection in near-critical fluids. Part 2. Weakly non-uniform heating

Dimitry Lyubimov (1) , Tanya Lyubimova (2) , Anatoliy Vorobev (1) , Abdelkader Mojtabi (3) , Bernard Zappoli (4)

1 Theoretical physics department (Perm, RUSSIA)
2 ICMM - Institute of Continuous Media Mechanics of the RAS
3 IMFT - Institut de mécanique des fluides de Toulouse
4 CNES - Centre National d'Études Spatiales [Toulouse]

The governing equations and effective boundary conditions to describe thermal vibrational convection in a near-critical fluid are derived with the help of the multiple-scale method and averaging procedure. In contrast to Part 1, this paper focuses on the effects of density non-homogeneities caused not by external heating but by vibrational and gravity stratifications due to the divergent mechanical compressibility of near-critical media. It is shown that vibrations generate non-homogeneities in the average temperature, which result in the onset of thermal convection even under isothermal boundary conditions. An agreement with the results of previous numerical and asymptotical analyses and with experiments is found.

Mots clés: Thermal convection; Vibrations; Isothermal boundary

Domaines: Mécanique des fluides [physics.class-ph]

Dimitry Lyubimov, Tanya Lyubimova, Anatoliy Vorobev, Abdelkader Mojtabi, Bernard Zappoli. Thermal vibrational convection in near-critical fluids. Part 2. Weakly non-uniform heating. Journal of Fluid Mechanics, 2006, 564, pp.185-196. ⟨10.1017/S002211200600142X⟩. ⟨hal-01946088⟩