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

9701967 Akylas 内重力波具有相当大的地球物理意义：大振幅内波扰动经常发生在深水和沿海地区以及低层大气的海洋温跃层中。 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，在深水中重力毛细管孤立波的产生以及非线性波群的振荡尾部辐射中发挥着重要作用。 主要目标是从物理和数学的角度理解分层流背景下的这种耦合机制。 这项研究工作的结果预计将有助于检测和控制各种应用中非线性波扰动的传播。 例如，在海洋环境中，内波活动的知识对于海底导航和深水离岸设施的设计非常重要。 在大气中，内波对于雷暴飑线的引发和组织、降雨的调节和大气污染物的扩散起着重要作用。 非线性脉冲还用于光纤和光交换装置中的数据高速传输；了解非线性脉冲的传播特性对于长距离传输无噪声信号至关重要。

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.