適切な支配方程式に基づく気体のベナール問題の再検討(流体工学,流体機械)

概要

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We revisit the Benard problem for a gas in the continuum limit. It was recently shown that the behavior of a gas with finite temperature difference is not described by the usual NS equations but by the SB equations, which are derived systematically from the Boltzmann equation in the continuum limit. The SB equations include the thermal-stress term which does not appear in the NS equations. In the present study, we investigate the linear stability of the quiescent state of the system on the basis of the SB equations and the results are compared with those on the basis of the NS equations. It is found that the critical Rayleigh number for the onset of instability is always smaller and growth rate of a disturbance is always larger in the framework of the SB equations. Thus, the thermal-stress term has a role of accelererating the Rayleigh-Taylor instability, and increasing the strength of thermal convection. These features are commonly observed not only for no-slip boundary conditions but also for free-slip boundary conditions.
2010-08-25