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

9701967阿基拉斯重力内波具有相当大的地球物理意义：海洋温跃层、深水和沿海地区以及低层大气中经常发生大幅度内波扰动。这项工作集中于内波群的动力学，特别是短尺度载流子振荡与群包络的耦合。这是一种完全非线性的机制，在深水重力-毛细管孤立波的产生和非线性波群对振荡尾巴的辐射中起着重要作用。主要目的是在分层流动的背景下，从物理和数学的角度理解这种耦合机制。这一研究工作的结果有望对各种应用中的非线性波动扰动的传播进行检测和控制。例如，在海洋环境中，关于内波活动的知识对海底航行和深水近海设施的设计很重要。在大气中，内波对雷暴锋线的形成和组织、降水的调节和大气污染物的扩散起着重要的作用。非线性脉冲也用于光纤和光交换设备中的高速数据传输；了解非线性脉冲的传播特性对于长距离无噪声信号的传输至关重要。

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.