根据精确或自洽平均流进行频率预测
Frequency prediction from exact or self-consistent meanflows
摘要：
已经提出了一些近似来估计基本的流体动力学量，特别是极限环的频率。其中之一，RZIF（为实零虚频），要求线性化关于平均流的控制方程，并估计频率作为前导特征值的虚部。进一步的简化，SCM（自洽模型），近似的平均流量，以及，作为唯一导致的非线性相互作用的领先的本征模式与本身。RZIF和SCM都被证明对圆柱尾流的典型情况是非常成功的。在这里，SCM被应用到热溶质对流，其中的超临界霍普夫分岔产生分支的驻波和行波。SCM是通过一个完整的牛顿法耦合的近似平均流和领先的本征模式。虽然RZIF属性验证的行波，SCM再现的非线性频率只有非常接近的分叉和另一个孤立的参数值的发病。因此，由主导模式引起的非线性相互作用不足以再现非线性平均场和频率。
英文摘要：
A number of approximations have been proposed to estimate basic hydrodynamic quantities, in particular the frequency of a limit cycle. One of these, RZIF (for Real Zero Imaginary Frequency), calls for linearizing the governing equations about the mean flow and estimating the frequency as the imaginary part of the leading eigenvalue. A further reduction, the SCM (for Self-Consistent Model), approximates the mean flow as well, as resulting only from the nonlinear interaction of the leading eigenmode with itself. Both RZIF and SCM have proven dramatically successful for the archetypal case of the wake of a circular cylinder. Here, the SCM is applied to thermosolutal convection, for which a supercritical Hopf bifurcation gives rise to branches of standing waves and traveling waves. The SCM is solved by means of a full Newton method coupling the approximate mean flow and leading eigenmode. Although the RZIF property is verified for the traveling waves, the SCM reproduces the nonlinear frequency only very near the onset of the bifurcation and for another isolated parameter value. Thus, the nonlinear interaction arising from the leading mode is insufficient to reproduce the nonlinear mean field and frequency.
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