横向加热圆柱环中的热对流
Thermal convection in a cylindrical annulus heated laterally
摘要：
在本文中，我们研究热对流不稳定性中出现的流体在一个圆柱形的环形加热横向。一旦施加水平温度梯度，就会出现对流状态。当温度梯度达到一个临界值时，可能发生稳态或振荡分叉。这个问题是仿照一种新的方法，它扩展了（numerico）中所描述的。Navier斯托克斯方程在原始变量公式中求解，并具有适当的压力边界条件。这是一个低阶公式，它在柱面坐标中引入了低阶奇点。用切比雪夫配置法对问题进行了离散化，并检验了其收敛性.得到的结果不仅与实验结果非常吻合，而且还提供了一个更深入的了解重要的物理参数发展的不稳定性，这是以前没有报道。
英文摘要：
In this paper we study thermoconvective instabilities appearing in a fluid within a cylindrical annulus heated laterally. As soon as a horizontal temperature gradient is applied a convective state appears. As the temperature gradient reaches a critical value a stationary or oscillatory bifurcation may take place. The problem is modelled with a novel method which extends the one described in (numerico). The Navier Stokes equations are solved in the primitive variable formulation, with appropriate boundary conditions for pressure. This is a low order formulation which in cylindrical coordinates introduces lower order singularities. The problem is discretized with a Chebyshev collocation method easily implemented and its convergence has been checked. The results obtained are not only in very good agreement with those obtained in experiments, but also provide a deeper insight into important physical parameters developing the instability, which has not been reported before.
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