On the stability of steady finite amplitude convection
On the stability of steady finite amplitude convection
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DOI：
10.1017/s0022112065001271
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发表时间：
1965-09
影响因子：
3.7
通讯作者：
A. Schlueter;D. Lortz;F. Busse
中科院分区：
文献类型：
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作者：
A. Schlueter;D. Lortz;F. Busse
从下面加热的水平流体层的静态可能变得不稳定。如果该层在水平方向上无限大，则Boussinesq方程允许有许多不同的定常解。本文提出了一种系统的方法，通过逐次逼近的方法得到有限振幅稳态解。事实证明，并非线性问题的每个解都是非线性问题的近似，但仍然存在无限多个有限振幅解。一个类似的程序已被应用到这些稳定的有限振幅的解决方案的稳定性问题的结果，三维的解决方案是不稳定的，但有一类二维流动是稳定的。该问题已被视为刚性和自由边界。
The static state of a horizontal layer of fluid heated from below may become unstable. If the layer is infinitely large in horizontal extent, the Boussinesq equations admit many different steady solutions. A systematic method is presented here which yields the finite-amplitude steady solutions by means of successive approximations. It turns out that not every solution of the linear problem is an approximation to the non-linear problem, yet there are still an infinite number of finite amplitude solutions. A similar procedure has been applied to the stability problem for these steady finite amplitude solutions with the result that three-dimensional solutions are unstable but there is a class of two-dimensional flows which are stable. The problem has been treated for both rigid and free boundaries.