Data set of all the figures from Stability of buoyant viscoelastic fluid flow in a vertical porous layer with horizontal throughflow

The stability of buoyancy-driven convection in a viscoelastic fluid saturating a vertical porous layer under the influence of a horizontal throughflow is studied. The viscoelastic behaviour is displayed by means of the Oldroyd-B type fluid, and its flow is represented through a suitable extension of Darcy's Law. The basic velocity and temperature fields turn out to be independent of viscoelastic rheology but are significantly influenced by throughflow. A linear stability analysis leads to a differential eigenvalue problem, which is numerically solved to obtain the neutral stability curves and the critical Darcy–Rayleigh number marking the onset of instability. The transition to instability is governed by the Péclet number and viscoelastic parameters, both of which influence the position of the neutral stability curve and the critical Darcy–Rayleigh number. The elasticity of the fluid primarily drives instability, with stress relaxation and strain retardation parameters exerting opposing effects. Though throughflow by itself does not render the system unstable, it profoundly influences the onset of instability once it arises—regardless of direction—by inducing both stabilizing and destabilizing effects.

本文研究了水平穿流作用下，充满垂直多孔介质层的粘弹性流体中的浮力驱动对流稳定性问题。本文采用Oldroyd-B型流体（Oldroyd-B type fluid）表征粘弹性流变行为，并通过达西定律（Darcy's Law）的合理拓展描述其流动特性。基础速度场与温度场与粘弹性流变特性无关，但受穿流的显著影响。通过线性稳定性分析推导得到微分特征值问题，借助数值方法求解该问题，最终获得中性稳定曲线与表征失稳起始的临界达西瑞利数。失稳转变过程由佩克莱特数（Péclet number）与粘弹性参数共同控制，二者均会影响中性稳定曲线的位置与临界达西瑞利数的取值。流体的弹性是诱发失稳的核心因素，应力松弛参数与应变延迟参数则呈现相反的调控效应。尽管穿流本身不会引发系统失稳，但无论流向如何，一旦系统出现失稳态势，穿流可通过同时诱导稳定与失稳效应，对失稳起始过程产生显著调控作用。