Parametric subharmonic instability of internal waves: locally confined beams versus monochromatic wavetrains
Parametric subharmonic instability of internal waves: locally confined beams versus monochromatic wavetrains
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内波的参数次谐波不稳定性：局部约束光束与单色波列
DOI：
10.1017/jfm.2014.509
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发表时间：
2014
影响因子：
3.7
通讯作者：
T. Akylas
中科院分区：
文献类型：
--
作者：
H. Karimi;T. Akylas
摘要连续层状流体中的内重力波列通常是不稳定的，这是三个共振相互作用的结果，在无粘性极限下，这种相互作用放大了频率等于下垫波频率的一半的短尺度扰动。这种所谓的参数亚谐不稳定(PSI)已经被广泛地研究了空间和时间的单色波。本文对具有局部约束空间轮廓的时谐平面波的PSI进行了渐近分析，试图了解这种波束在PSI方面与单色平面波有何不同。讨论集中在一个耦合演化方程组上，该方程组控制了在几乎无粘的均匀分层的Boussinesq流体中小幅度波束与短尺度亚谐波包的相互作用。对于具有一般局域化轮廓的光束，发现在亚谐微扰与光束重叠的有限时间内，三分量相互作用不足以产生不稳定性。另一方面，对于其轮廓包括受局部限制包络调制的正弦载波的准单色波束，如果光束足够宽，则PSI是可能的。在这种情况下，提出了一个稳定性判据，在给定的流动条件下，它提供了小幅度光束产生不稳定性所必须包含的最小载波波长数目。
Abstract Internal gravity wavetrains in continuously stratified fluids are generally unstable as a result of resonant triad interactions which, in the inviscid limit, amplify short-scale perturbations with frequency equal to one half of that of the underlying wave. This so-called parametric subharmonic instability (PSI) has been studied extensively for spatially and temporally monochromatic waves. Here, an asymptotic analysis of PSI for time-harmonic plane waves with locally confined spatial profile is made, in an effort to understand how such wave beams differ, in regard to PSI, from monochromatic plane waves. The discussion centres upon a system of coupled evolution equations that govern the interaction of a small-amplitude wave beam with short-scale subharmonic wavepackets in a nearly inviscid uniformly stratified Boussinesq fluid. For beams with general localized profile, it is found that triad interactions are not strong enough to bring about instability in the limited time that subharmonic perturbations overlap with the beam. On the other hand, for quasi-monochromatic wave beams whose profile comprises a sinusoidal carrier modulated by a locally confined envelope, PSI is possible if the beam is wide enough. In this instance, a stability criterion is proposed which, under given flow conditions, provides the minimum number of carrier wavelengths a beam of small amplitude must comprise for instability to arise.
影响因子：
--
作者：
T. Hibiya;M. Nagasawa;Y. Niwa
通讯作者：
T. Hibiya;M. Nagasawa;Y. Niwa