论文标题
在垂直多孔层中平行流的稳定性，环形横截面
On the stability of parallel flow in a vertical porous layer with annular cross-section
论文作者
论文摘要
研究了带有环形横截面的垂直多孔层中浮力平行流的线性稳定性。垂直圆柱边界保持在不同的均匀温度下，并被认为是不可渗透的。基于线性化处理方程的数值解，排除了对流细胞线性不稳定性的出现。该结果延伸到环形几何形状，众所周知的g定理在垂直的多孔平面平板上不可能不稳定性，其边界不可渗透并且温度不同。通过评估正常模式扰动的生长速率并表明其符号为负，这意味着基本流动的渐近稳定性，从而在数值上接近了吉尔定理到环形域的扩展。同意支持缺乏线性不稳定性的论点是由对垂直边界处的不渗透条件放松并通过压力的罗宾边界条件模拟部分渗透率的情况的情况。有了部分渗透的边界，出现的不稳定性采用轴对称正常模式的形式。
The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross-section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures and they are assumed to be impermeable. The emergence of linear instability by convection cells is excluded on the basis of a numerical solution of the linearised governing equations. This result extends to the annular geometry the well-known Gill's theorem regarding the impossibility of convective instability in a vertical porous plane slab whose boundaries are impermeable and isothermal with different temperatures. The extension of Gill's theorem to the annular domain is approached numerically by evaluating the growth rate of normal mode perturbations and showing that its sign is negative, which means asymptotic stability of the basic flow. A concurring argument supporting the absence of linear instability arises from the investigation of cases where the impermeability condition at the vertical boundaries is relaxed and a partial permeability is modelled through Robin boundary conditions for the pressure. With partially permeable boundaries, an instability emerges which takes the form of axisymmetric normal modes.
