服务于遥感探测的深海内波模型解析研究

This project will combine the demand of the information field and methods in mathematics，carry out the analytical research on deep oceanic internal wave models and establish the deep oceanic internal waves detection model, so that the analytic results can serve the remote sensing detection of deep oceanic internal waves better. (1)We will discuss the integrability of internal wave BO model in continuous stratified deep ocean and explore the methods for its analytic solution.We will also analyze the propagation characteristics of deep oceanic internal waves and the effect of marine environments on the propagation of deep oceanic internal waves.(2)We will analyze the physical background related to NLS model, discuss the relationship between nonlinear and dispersion effects and then solve the analytic solution of NLS model with Darboux transformation and its expansion, and analyze the propagation properties of oceanic internal waves.(3)Combining the field test and remote sensing data, we will solve the models of internal waves in finite water depth analytically and discuss the applicable condition and adaptability of the models in deep ocean. What's more, we will modify and generalize the models to adapt to the description of deep oceanic internal waves.(4)We will construct models for deep oceanic internal wave detection with the analytic results and internal wave remote sensing imaging mechanism. Using the remote sensing images of internal waves,its parameters will be inversed and propagation regularity in relevant oceanic area will be obtained and the analysis will be given comparing with the field test data. The results can provide basis for the prediction of deep oceanic internal waves.

本项目拟结合信息领域的需求和数学领域的方法，对深海内波模型进行解析研究，建立深海内波探测模型，使解析研究结果更好地服务于深海内波遥感探测。(1)讨论连续分层深海内波BO模型的可积性质，研究BO模型的解析求解方法，分析深海内波的传播特性和海洋环境因素对于深海内波传播的影响;(2)分析NLS类模型中相关物理背景，讨论非线性效应与频散效应的关系，利用并拓展Darboux变换法求解NLS类模型的解析解并分析深海内波的传播性质;(3)与实测和遥感数据相结合，解析求解有限水深内波模型，讨论模型在深海海域的适用条件和适用性，并对模型进行修正和推广，以适应于描述深海内波的传播;(4)利用深海内波解析结果与内波遥感成像机理相结合构建深海内波探测模型，利用内波遥感图像进行参数反演，给出相关海域内波传播规律，与现场测量结果进行对比分析，为深海内波的传播预测提供依据。

随着我国经济、社会和国防建设的迅速发展，对深远海的资源开发和环境监测提出了迫切的需求。本项目以深海非线性内波模型的解析研究为基础，服务于深海内波的遥感探测，具有信息处理、应用数学与物理海洋等多学科交叉的特性。项目针对深海内波研究的需求以及深海非线性模型之间的差异，通过拓展孤立子理论中相关的解析方法，解析研究了海洋内波的相关模型，将解析研究结果应用于遥感探测，使解析研究结果更好地服务于深海内波遥感探测，这可为分析海水动力学过程和深海内波的预测预报提供依据。项目利用Darboux变换、双线性等方法解析研究了适合于描述深海内波传播的BO模型、NLS类模型的解析解及其传播特征分析。研究了KdV类模型的解析解，并讨论了不同参数取值下各类非线性波的传播演化特性。拓展了适合于内波模型求解方法，探索了Darboux变换、Lie群变换法、双线性方法和Bell多项式方法在非线性波动模型解析研究中的应用。对从SAR遥感图像中提取内波信号的EEMD算法进行了研究，为更好的提取内波信息提供了有效的方法支持。基于KP方程解析解和SAR图进行了内波参数反演，基于实测数据对南海北部内波发生情况进行统计分析。