Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow.
Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow.
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绝对不稳定状态下的模式选择作为非线性特征值问题：轴流中的泰勒涡。
DOI：
10.1103/physreve.53.4764
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
Schmitz
中科院分区：
文献类型：
--
作者：
Büchel;Luecke;Roth;Schmitz
一个独特的模式选择在绝对不稳定的制度的驱动，非线性，开放的流系统进行了分析：旋转对称涡的时空结构，传播下游的环形旋转泰勒-Couette系统由于外部施加的轴向通流的研究两个不同的轴向边界条件在入口和出口。详细的定量结果的振荡频率，波数的轴向分布，和时间傅立叶振幅的传播的涡模式通过数值模拟的Navier-Stokes方程的结果进行了比较适当的Ginzburg-Landau振幅方程近似，也与实验。与没有通流的系统中的静止模式不同，传播涡的时空结构与参数历史、初始条件和系统长度无关。然而，除了内筒的驱动速率和通流速率之外，它们还取决于轴向边界条件。我们的振幅方程的分析表明，模式选择可以描述为一个非线性的本征值问题的频率是本征值。复振幅作为相应的本征函数描述了强度和波数的轴向结构。Navier-Stokes方程和振幅方程之间的结构动力学的小的但特征的差异主要是由于不同的色散关系。接近边界之间的绝对和对流不稳定的特征值问题变得有效的线性和选择机制的线性前传播的方法。
A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating Taylor-Couette system due to an externally imposed axial through-flow are investigated for two different axial boundary conditions at the inlet and outlet. Detailed quantitative results for the oscillation frequency, the axial profile of the wave number, and the temporal Fourier amplitudes of the propagating vortex patterns obtained by numerical simulations of the Navier-Stokes equations are compared with results of the appropriate Ginzburg-Landau amplitude equation approximation and also with experiments. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system length. They do, however, depend on the axial boundary conditions in addition to the driving rate of the inner cylinder and the through-flow rate. Our analysis of the amplitude equation shows that the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. The complex amplitude being the corresponding eigenfunction describes the axial structure of intensity and wave number. Small, but characteristic differences in the structural dynamics between the Navier-Stokes equations and the amplitude equation are mainly due to the different dispersion relations. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that of linear front propagation.