MODULATED WAVES IN TAYLOR-COUETTE FLOW .1. ANALYSIS
MODULATED WAVES IN TAYLOR-COUETTE FLOW .1. ANALYSIS
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DOI：
10.1017/s0022112092000673
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发表时间：
1992-01-01
影响因子：
3.7
通讯作者：
MARCUS, PS
中科院分区：
文献类型：
--
作者：
COUGHLIN, KT;MARCUS, PS
本文对具有圆对称边界条件的旋转流动中的时间周期旋转波到准周期调制波的转变进行了数学分析，并应用于同心旋转圆柱之间的流动(Taylor Couette流)。准周期流动(调制波动涡旋流)在任意坐标系中用两个无公度的基波时间频率来描述，但在适当的旋转坐标系中流动是周期的。调制的方位波长可能不同于下面旋转波的方位波长：因此，流动状态也可以用两个方位波数来描述。一个频率和一个波数由波状态确定，但是没有简单的物理特性与调制参数相关联。目前关于调制波的文献既显示了相互冲突的数学表示，又显示了性质不同的调制类型。本文利用Floquet理论导出了所有调制波的唯一泛函形式，并证明了时空对称性是直接遵循的。流可以写成两个阶段(theta-c1t、theta-c2t)的不可分函数。我们证明了Taylor Couette流中调制波解的不同分支不是由对称性来区分的，而是由解的c1、c2的数值范围和解的谱幅度来区分的。与调制相关的方位波数具有唯一的物理定义，但不直接表示为调制流的空间对称性。由于调制波一般应该出现在具有旋转对称性的系统中，因此这种分析的应用范围超出了Taylor Couette流。
We present a mathematical analysis of the transition from temporally periodic rotating waves to quasi-periodic modulated waves in rotating flows with circularly symmetric boundary conditions, applied to the flow between concentric, rotating cylinders (Taylor Couette flow). Quasi-periodic flow (modulated wavy vortex flow) is described by two incommensurate, fundamental, temporal frequencies in an arbitrary frame, but the flow is periodic in the appropriate rotating frame. The azimuthal wavelength of the modulation may be different to that of the underlying rotating wave: hence the flow state is described by two azimuthal wavenumbers as well. One frequency and one wavenumber are determined by the wave state, but no simple physical properties have vet, been associated with the parameters of the modulation. The current literature on modulated waves displays both conflicting mathematical representations and qualitatively different kinds of modulation. In this paper we use Floquet theory to derive the unique functional form tor all modulated waves and show that the space time symmetry properties follow directly. The flow can be written as a non-separable function of the two phases (theta-c1t, theta-c2t). We show that different branches of modulated wave solutions in Taylor Couette flow are distinguished not by symmetry but by the ranges of the numerical values of c1, c2, and the spectral amplitudes of the solution. The azimuthal wavenumber associated with the modulation has a unique physical definition but is not directly expressed in the spatial symmetry of the modulated flow. Because modulated waves should occur generically in systems with rotational symmetry, this analysis has application beyond Taylor Couette flow.