The paper deals with the study of effect of gravity modulation on double-diffusive convection in a dielectric liquid for the cases of rigid-rigid and free-free boundaries. Using a modified Venezian approach, expressions for the Rayleigh number and its correction are determined. Fourier–Galerkin expansion is employed for a weakly nonlinear stability analysis and this results in a fifth-order Lorenz system that retains the structure of the classical one in the limiting case. A local nonlinear stability analysis using the method of multiscales leads to the time-periodic Ginzburg–Landau equation from the time-periodic generalized Lorenz system and the numerical solution of this simpler equation helps in quantifying unsteady heat and mass transports. Influence of various non-dimensional parameters (Lewis number, solutal Rayleigh number, electrical Rayleigh number and Prandtl number), amplitude and frequency of gravity modulation on onset of convection and heat and mass transports is discussed. The study reveals that the influence of gravity modulation is to stabilize the system and enhance heat and mass transports. The results from free-free boundaries are qualitatively similar to that of rigid-rigid boundaries. Further, it is shown that in the case of free-free boundaries the heat and mass transports are less compared to those of rigid-rigid boundaries.

中文翻译：

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重力调制对介电液体中稳态双扩散对流的线性、弱非线性和局部非线性稳定性分析的影响

本文针对刚性-刚性和自由自由边界的情况，研究了重力调制对介电液体中双扩散对流的影响。使用改进的威尼斯方法，确定瑞利数及其校正的表达式。傅立叶-伽辽金展开式用于弱非线性稳定性分析，这导致五阶洛伦兹系统在极限情况下保留经典系统的结构。使用多尺度方法的局部非线性稳定性分析从时间周期广义洛伦兹系统导出时间周期 Ginzburg-Landau 方程，这个更简单方程的数值解有助于量化不稳定的热量和质量传输。各种无量纲参数的影响（刘易斯数、溶质瑞利数、电瑞利数和普朗特数），讨论了对流开始时重力调制的幅度和频率以及热量和质量传输。研究表明，重力调制的影响是稳定系统并增强热量和质量传输。自由自由边界的结果与刚性-刚性边界的结果在性质上相似。此外，结果表明，在自由边界的情况下，与刚性-刚性边界相比，热量和质量传输较少。自由自由边界的结果与刚性-刚性边界的结果在性质上相似。此外，结果表明，在自由边界的情况下，与刚性-刚性边界相比，热量和质量传输较少。自由自由边界的结果与刚性-刚性边界的结果在性质上相似。此外，结果表明，在自由边界的情况下，与刚性-刚性边界相比，热量和质量传输较少。