Renaudière de Vaux Sébastien, Zamansky Rémi, Bergez Wladimir, Tordjeman Philippe, Haquet Jean-François
Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS-INPT-UPS, Toulouse, France.
CEA, DEN, Cadarache, SMTA/LPMA, F13108 St, Paul lez Durance, France.
Eur Phys J E Soft Matter. 2017 Jan;40(1):13. doi: 10.1140/epje/i2017-11499-2. Epub 2017 Jan 30.
We investigate the transient and stationary buoyant motion of the Rayleigh-Bénard instability when the fluid layer is subjected to a vertical, steady magnetic field. For Rayleigh number, Ra, in the range 10-10, and Hartmann number, Ha, between 0 and 100, we performed three-dimensional direct numerical simulations. To predict the growth rate and the wavelength of the initial regime observed with the numerical simulations, we developed the linear stability analysis beyond marginal stability for this problem. We analyzed the pattern of the flow from linear to nonlinear regime. We observe the evolution of steady state patterns depending on [Formula: see text] and Ha. In addition, in the nonlinear regime, the averaged kinetic energy is found to depend on Ra and to be independent of Ha in the studied range.
当流体层受到垂直、稳定的磁场作用时，我们研究了瑞利 - 贝纳德不稳定性的瞬态和稳态浮力运动。对于瑞利数(Ra)在(10^3 - 10^6)范围内，以及哈特曼数(Ha)在(0)到(100)之间的情况，我们进行了三维直接数值模拟。为了预测数值模拟中观察到的初始阶段的增长率和波长，我们针对此问题开展了超越边际稳定性的线性稳定性分析。我们分析了从线性到非线性状态的流动模式。我们观察到稳态模式的演变取决于(\cdots)（公式：见原文）和(Ha)。此外，在非线性状态下，发现平均动能取决于(Ra)，并且在所研究的范围内与(Ha)无关。
