Mathematical Sciences: Nonlinear Coupling of Long Internal Waves with Small-Scale Disturbances

小行星9701967 重力内波具有相当大的地球物理意义： 海洋中经常发生大幅内波扰动 在深水和沿海地区，以及 低层大气 这一努力的重点是内部波的动力学 特别是短尺度载体的耦合 与群的包络线的振荡。 这是一个完全非线性的 在生成中起重要作用的机制 重力-毛细孤立波在深水和辐射 非线性波群的振荡尾。 主要目标是 在分层流动的背景下理解这种耦合机制， 从物理和数学的角度来看。 这项研究工作的结果预计将有助于 检测和控制非线性波浪扰动的传播 在各种应用中。 例如，在海洋环境中， 内波活动知识在海底导航中是重要的 以及深水近海设施的设计。 在大气中， 内波在启动和组织中起重要作用 雷暴飑线的形成、降水的调制和雷暴的形成 大气污染物的扩散。 非线性脉冲也用于 在光纤中和光通信中高速数据传输 开关器件;了解的传播特性 非线性脉冲对于无噪声信号的传输至关重要 在很长的距离。

9701967 Akylas Internal gravity waves are of considerable geophysical interest: large-amplitude internal wave disturbances frequently occur in the ocean thermocline both in deep water and in coastal regions, as well as in the lower atmosphere. This effort focuses on the dynamics of internal-wave groups, particularly the coupling of the short-scale carrier oscillations with the envelope of the group. This is a fully nonlinear mechanism that plays an important part in the generation of gravity-capillary solitary waves on deep water and in the radiation of oscillatory tails by nonlinear wave groups. The main objective is to understand this coupling mechanism in the context of stratified flows, both from a physical and a mathematical point of view. The results of this research effort are expected to be useful in detecting and controlling the propagation of nonlinear wave disturbances in various applications. In the ocean environment, for instance, knowledge of internal-wave activity is important in under-sea navigation and in the design of deep-water offshore facilities. In the atmosphere, internal waves play an important part in the initiation and organization of thunderstorm squall lines, the modulation of rainfall and the dispersal of atmospheric pollutants. Nonlinear pulses are also used in high-speed transmission of data in optical fibers and in optical switching devices; understanding the propagation characteristics of nonlinear pulses is essential to the transmission of noise-free signals over long distances.