Nonlinear Wave Dynamics in Stratified Flows

点击翻译按钮获取中文摘要

Two problems of gravity wave propagation in stratified flows will be studied: the propagation of internal wave beams and the resonant interaction of nonlinear modulated wavetrains with the induced mean flow. Since gravity provides a preferred direction, internal wave disturbances generated by an oscillatory source are anisotropic; rather than cylindrical fronts, they form straight beams stretching radially outwards. The propagation characteristics of such beams will be studied under various flow conditions using asymptotic and numerical models. Particular emphasis will be placed on three-dimensional and non-axisymmetric beams for which nonlinear effects are most pronounced. Secondly, a theoretical study will be made of the so-called resonant self-acceleration of modulated wavetrains; this strong nonlinear interaction between the wavetrain envelope and the induced horizontal mean flow can cause instability and breakdown of nearly vertically propagating wavetrains. Although not as familiar from everyday experience as ocean surface waves, internal gravity waves are in fact ubiquitous in oceans, lakes and in the atmosphere, where they play an important part in transferring momentum and energy. Internal gravity wave beams in particular are often triggered by thunderstorms, and there is evidence from numerical simulations and field observations that a significant component of gravity wave activity in the atmosphere is in the form of beam-like structures. Understanding the propagation characteristics of internal gravity wave beams will thus prove useful in weather forecasting. This award is being jointly funded by the Division of Mathematical Sciences and the Directorate for Engineering as part of the Mathematical Sciences Priority Area.