Instabilities of the natural convection around a cone in thermally stratified medium,Physical Review E

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Instabilities of the natural convection around a cone in thermally stratified medium
Physical Review E ( IF 2.2 ) Pub Date : 2022-09-14 , DOI: 10.1103/physreve.106.035102
Yue Xiao ₁ , Yi Li ₁ , Moli Zhao ₁ , Shaowei Wang ₁

Affiliation

In this paper, we provide a mathematical description of the onset of instability for buoyancy-driven flow around a cone. The self-similar solutions of the basic flow are derived, where the ambient fluid and the cone have independent temperature gradients. The linear instability properties are investigated by utilizing the Chebyshev collocation method. It is demonstrated that the neutral curves have a two-lobed structure and that changing the Grashof number has only quantitative influence on stability. The critical streamwise location increases when the half-apex angle is increased, and the unstable range of the wave number diminishes. According to the examination of eigenfunction profiles and the progression of the two spatial branches in the

(α_{i}, α_{r})

planes, the primary instabilities on the surface of cone are identified as type-I mode and type-II mode. The energy analysis is investigated for a typical situation to gain a physical insight, where it is demonstrated that besides the viscous dissipation, the streamline curvature and buoyancy-driven effects are dominant for the type-I mode while inviscid effect plays an essential role in type II. These encouraging results are expected to be conducive to understanding buoyancy-driven systems.

中文翻译：

热分层介质中锥体周围自然对流的不稳定性

在本文中，我们提供了对围绕锥体的浮力驱动流动的不稳定性开始的数学描述。导出了基本流的自相似解，其中环境流体和锥体具有独立的温度梯度。利用切比雪夫搭配法研究了线性不稳定性特性。证明了中性曲线具有双叶结构，并且改变 Grashof 数对稳定性仅具有定量影响。随着半顶角的增加，临界流向位置增加，波数的不稳定范围减小。根据特征函数剖面的检查和两个空间分支在