Nonlinear Dispersive Waves and Applications to Geophysical Fluid Flows

非线性色散波及其在地球物理流体流动中的应用

• 批准号: 0104329
• 负责人: Roberto Camassa
• 金额: $ 17.35万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-15 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0104329&HistoricalAwards=false
• 关键词: Nonlinear; Dispersive; Waves; Applications; Geophysical

This project is organized around two leading themes in internal gravity wave propagation in stratified fluids: (a) interplay between nonlinearity and dispersion, and (b) instabilities and resonances. Within the first theme, the long term goal is to provide a model of internal waves in layered stratification that correctly accounts for dispersion and high nonlinearity, to be used in alternative to the currently adopted non-dispersive and weakly nonlinear models. The aim is to retain the advantage of the simplicity of these theories with respect to the full Euler (or Navier-Stokes) governing motion equations, while still maintaining the ability to describe wave dynamics of practical interest. Highly nonlinear regimes often generate instabilities. The causes and evolution of these instabilities for fully nonlinear internal waves are the focus within the second theme. In particular, stability criteria based on the Howard-Miles theorem for stationary shear flows and parametric instability occurring at stable Richardson's number will be revisited in the context of internal gravity waves.This research focuses on an area of wave propagation which has widespread atmospheric and oceanic applications, and, therefore, large societal implications. For instance, large internal waves generated by wind forcing of the upper ocean may have a strong feedback effect on the intensity of hurricanes. Thus, numerical codes based on models capable of representing accurately large amplitude waves and their dispersive behavior (responsible for the spreading of wave energy over increasingly larger regions) can play an important role in hurricane forecasts, at little additional cost with respect to the currently employed hydrostatic codes. The award will support work that will help establish the theoretical and technical foundations of such improved computational codes.

本项目围绕分层流体中重力内波传播的两个主要主题进行组织：（a）非线性和色散之间的相互作用，以及（B）不稳定性和共振。 在第一个主题中，长期目标是提供一个分层分层的内波模型，该模型正确地考虑了色散和高非线性，用于替代目前采用的非色散和弱非线性模型。 其目的是保留这些理论相对于完整的欧拉（或Navier-Stokes）运动方程的简单性的优点，同时仍然保持描述实际感兴趣的波动动力学的能力。 高度非线性的区域通常会产生不稳定性。 完全非线性内波不稳定性的原因和演化是第二个主题的重点。 特别是，稳定性标准的基础上的霍华德-迈尔斯定理的定常剪切流和参数不稳定性发生在稳定的理查森数将重新审视的背景下，内部gravitationwave.This研究的重点是波传播的一个领域，具有广泛的大气和海洋的应用，因此，大的社会影响。 例如，上层海洋风力产生的大型内波可能对飓风的强度产生强烈的反馈效应。 因此，基于能够准确表示大振幅波及其色散行为（负责波能在越来越大的区域内传播）的模型的数值代码可以在飓风预报中发挥重要作用，而与目前采用的流体静力学代码相比，成本几乎没有增加。 该奖项将支持有助于建立这种改进的计算代码的理论和技术基础的工作。