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

Akylas内重力波具有重要的地球物理意义：在深海和沿海地区的海洋温跃层以及低层大气中经常发生大振幅内波扰动。这项工作的重点是内波群的动力学，特别是短尺度载波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-毛细孤立波的产生和非线性波群振荡尾的辐射中起着重要作用。主要目标是从物理和数学的角度来理解分层流背景下的这种耦合机制。本研究成果有望在各种应用中检测和控制非线性波扰动的传播。例如，在海洋环境中，对内波活动的了解对于海底航行和深水离岸设施的设计非常重要。在大气中，内波在雷暴飑线的形成和组织、降雨的调节和大气污染物的扩散等方面起着重要作用。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无噪声信号的长距离传输至关重要。

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.