Remarks on nonlinear relation among phases and frequencies in modulational instabilities of parallel propagating Alfvén waves
Remarks on nonlinear relation among phases and frequencies in modulational instabilities of parallel propagating Alfvén waves
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DOI：
10.5194/npg-13-425-2006
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发表时间：
2006-08
影响因子：
2.2
通讯作者：
Y. Nariyuki;T. Hada
中科院分区：
文献类型：
--
作者：
Y. Nariyuki;T. Hada
抽象。在一维无耗散无强迫流体系统中，讨论了圆偏振Alfven波调制不稳定性中频率和相位之间的非线性关系。我们表明，相位相干的产生是阿尔芬波的调制不稳定性的自然后果。此外，我们定量评估的强度波波相互作用的双相干，也通过计算波模式之间的能量流，并证明了能量流是直接相关的相位相干的产生。我们首先讨论了微分非线性薛定谔（DNLS）方程中的调制不稳定性，DNLS方程是Hall MHD系统的一个子集，包含了右旋和左旋极化的准平行Alfven波。在这个模型中，主要的非线性过程是四波相互作用，其中四波共振可以交换能量。通过数值积分DNLS方程与周期性边界条件，并通过评估四波之间的相对相位，我们表明，相位相干时产生的四波之间的能量交换。结果，相干结构（孤子）出现在真实的空间中，而在波频和波数的相空间中，波功率被视为围绕直线分布。线的斜率对应于相干结构的传播速度。对具有周期性边界条件的Hall-MHD系统进行数值时间积分，发现横模和纵模的波功率在色散关系相空间中呈一条直线排列，表明Hall-MHD系统中实现了横、纵波模之间的有效能量交换.纵波模式的产生违反了推导DNLS时采用的假设，例如准静态近似，因此DNLS和Hall-MHD模型中阿尔芬调制不稳定性的长期演化显着不同，尽管初始等离子体和母波参数的选择方式使得调制不稳定性是各种参数不稳定性中最主要的不稳定性。其中一个最重要的特点，只出现在霍尔-MHD模型是由有质动力密度波动驱动的声波的产生。讨论了在真实的空间中，波模间的色散关系、能量交换和波形相位相干性之间的关系。并对今后的相关问题进行了讨论。
Abstract. Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfven waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of phase coherence is a natural consequence of the modulational instability of Alfven waves. Furthermore, we quantitatively evaluate intensity of wave-wave interaction by using bi-coherence, and also by computing energy flow among wave modes, and demonstrate that the energy flow is directly related to the phase coherence generation. We first discuss the modulational instability within the derivative nonlinear Schrodinger (DNLS) equation, which is a subset of the Hall-MHD system including the right- and left-hand polarized, nearly degenerate quasi-parallel Alfven waves. The dominant nonlinear process within this model is the four wave interaction, in which a quartet of waves in resonance can exchange energy. By numerically time integrating the DNLS equation with periodic boundary conditions, and by evaluating relative phase among the quartet of waves, we show that the phase coherence is generated when the waves exchange energy among the quartet of waves. As a result, coherent structures (solitons) appear in the real space, while in the phase space of the wave frequency and the wave number, the wave power is seen to be distributed around a straight line. The slope of the line corresponds to the propagation speed of the coherent structures. Numerical time integration of the Hall-MHD system with periodic boundary conditions reveals that, wave power of transverse modes and that of longitudinal modes are aligned with a single straight line in the dispersion relation phase space, suggesting that efficient exchange of energy among transverse and longitudinal wave modes is realized in the Hall-MHD. Generation of the longitudinal wave modes violates the assumptions employed in deriving the DNLS such as the quasi-static approximation, and thus long time evolution of the Alfven modulational instability in the DNLS and in the Hall-MHD models differs significantly, even though the initial plasma and parent wave parameters are chosen in such a way that the modulational instability is the most dominant instability among various parametric instabilities. One of the most important features which only appears in the Hall-MHD model is the generation of sound waves driven by ponderomotive density fluctuations. We discuss relationship between the dispersion relation, energy exchange among wave modes, and coherence of phases in the waveforms in the real space. Some relevant future issues are discussed as well.