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

点击翻译按钮获取中文摘要

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.