Stability of internal gravity wave beams to three-dimensional modulations
Stability of internal gravity wave beams to three-dimensional modulations
复制标题
内部重力波束对三维调制的稳定性
DOI：
10.1017/jfm.2013.527
复制
发表时间：
2013
影响因子：
3.7
通讯作者：
T. Akylas
中科院分区：
文献类型：
--
作者：
Takeshi Kataoka;T. Akylas
摘要讨论了具有局部受限空间轮廓的均匀平面内波束在恒浮力频率层状流体中的线性稳定性。假定长波相对于束宽有扰动，相应的本征值问题可渐近解。在此极限下，只有沿波束方向和水平横向变化的倾斜扰动才会出现不稳定性。不稳定的机制是波束和三维扰动之间的一次谐和平均共振相互作用，三维微扰包括时间调和分量、波束频率和平均流。特别是在一个方向上传输能量的渐进光束，如果光束陡度超过某个阈值，则是不稳定的，而纯站立光束即使在无限小的陡度下也是不稳定的。这种三维调制不稳定性的一个显著特征是在距离光束附近很远的地方产生了水平平均环流。
Abstract The linear stability of uniform, plane internal wave beams with locally confined spatial profile, in a stratified fluid of constant buoyancy frequency, is discussed. The associated eigenvalue problem is solved asymptotically, assuming perturbations of long wavelength relative to the beam width. In this limit, instability is found only for oblique disturbances which vary in the along-beam and the horizontal transverse directions. The mechanism of instability is a first-harmonic–mean resonant interaction between the underlying wave beam and three-dimensional perturbations that comprise a time-harmonic component, with the beam frequency, and a mean flow. Progressive beams which transport energy in one direction, in particular, are unstable if the beam steepness exceeds a certain threshold value, whereas purely standing beams are unstable even at infinitesimal steepness. A distinguishing feature of this three-dimensional modulational instability is the generation of circulating horizontal mean flows at large distances from the vicinity of the beam.