Instability of pole solutions for planar propagating flames in sufficiently large domains
Instability of pole solutions for planar propagating flames in sufficiently large domains
复制标题
足够大的域中平面传播火焰的极解的不稳定性
DOI：
10.1088/1364-7830/2/1/002
复制
发表时间：
1998
影响因子：
1.3
通讯作者：
G. Sivashinsky
中科院分区：
文献类型：
--
作者：
M. Rahibe;N. Aubry;G. Sivashinsky
众所周知，描述流体动力学不稳定平面火焰锋动力学的偏微分方程（PDE）具有精确的极点解，对于这些解，PDE可简化为一组常微分方程（ODE）。然而，悖论在于这样一个事实，即常微分方程组不允许在复平面上出现新的极点，也不允许在物理空间中形成实验中观察到的尖点。因此，PDE本身的有效性受到质疑。我们在这里表明，偏微分方程和常微分方程之间的差异是由于不稳定的精确极点解的偏微分方程。在以前的工作中，我们已经报告说，最精确的极点解决方案确实是不稳定的偏微分方程，但对于每个相对较小的长度L的间隔，仍然有一个解决方案（平移对称），这是中性稳定。后者是一个单峰，合并的解决方案，其中极点（其数量是最大的）是稳定的。前面经历分叉作为dom的长度.
It is well known that the partial differential equation (PDE) describing the dynamics of a hydrodynamically unstable planar flame front has exact pole solutions for which the PDE reduces to a set of ordinary differential equations (ODEs). The paradox, however, lies in the fact that the set of ODEs does not permit the appearance of new poles in the complex plane, or the formation of cusps in the physical space, as observed in experiments. The validity of the PDE itself has thus been questioned. We show here that the discrepancy between the PDE and the ODEs is due to the instability of exact pole solutions for the PDE. In previous work, we have reported that most exact pole solutions are indeed unstable for the PDE but, for each interval of relatively small length L, there remains one solution (up to translation symmetry) which is neutrally stable. The latter is a one-peak, coalescent solution for which the poles (whose number is maximal) are steady. The front undergoes bifurcations as the length of the dom...