Department of Mathematics, Guru Nanak Dev University, Amritsar-143005, Punjab, India.
Phys Rev E. 2023 Apr;107(4-2):045104. doi: 10.1103/PhysRevE.107.045104.
A parametric instability of an incompressible, viscous, and Boussinesq fluid layer bounded between two parallel planes is investigated numerically. The layer is assumed to be inclined at an angle with the horizontal. The planes bounding the layer are subjected to a time-periodic heating. Above a threshold value, the temperature gradient across the layer leads to an instability of an initially quiescent state or a parallel flow, depending upon the angle of inclination. Floquet analysis of the underlying system reveals that under modulation, the instability sets in as a convective-roll pattern executing harmonic or subharmonic temporal oscillations, depending upon the modulation, the angle of inclination, and the Prandtl number of the fluid. Under modulation, the onset of the instability is in the form of one of two spatial modes: the longitudinal mode and the transverse mode. The value of the angle of inclination for the codimension-2 point is found to be a function of the amplitude and the frequency of modulation. Furthermore, the temporal response is harmonic, or subharmonic, or bicritical depending upon the modulation. The temperature modulation offers good control of time-periodic heat and mass transfer in the inclined layer convection.
我们对不可压缩粘性 Boussinesq 流体层在两个平行平面之间的参数不稳定性进行了数值研究。该层与水平方向成一定角度。层的两个边界平面受到周期性的加热。超过某个阈值时，层内的温度梯度会导致初始静止状态或平行流失稳，具体取决于倾斜角度。对基础系统的 Floquet 分析表明，在调制下，不稳定性表现为对流-涡旋模式，执行谐波或亚谐波时间振荡，具体取决于调制、倾斜角度和流体的普朗特数。在调制下，不稳定性的发生有两种空间模式之一：纵向模式和横向模式。二维点的倾斜角度值是调制幅度和频率的函数。此外，时间响应是谐波、亚谐波还是双临界，取决于调制。温度调制为倾斜层对流中的周期性热和质量传递提供了良好的控制。
