论文总字数：14412字

摘 要

本文研究基于海浪谱的粗糙海面建模，蒙特卡罗方法对随机粗糙海面进行建模。实验所用方法基于Matlab平台FFT实现海浪谱和蒙特卡罗方法的建模；分析海面形状随风场变化的规律等多种技术方法从海面能量角度，基于海浪谱模型利用蒙特卡罗方法建模随机粗糙海面，并分析海面的粗糙度随海面风场的变化，感性和理性认识海浪谱和随机粗糙面之间的关系。本次模拟实验结果中表明：

（1）对粗其中两个参数的变化，，变化的周期横向变化特征由相关长度来确定。（2）Apel谱和种谱和Elfouhaily（3）随着风速的增加，模拟的海面由平缓到起伏较大 基于Apel谱和Elfouhaily谱在不同风速5m/s和10m/s下的海面理论值和粗糙面频谱的多次平均值相吻合，这说明基于该粗糙面功率谱模拟的随机粗糙面与理论值是一致的。

关键词：海浪谱；粗糙海面建模；蒙特卡罗方法构建；风场的变化

Modeling and analysis of rough sea surface based on wave spectrum

Abstract

In this paper, rough sea surface modeling based on wave spectrum is studied, and stochastic rough sea surface is modeled by Monte Carlo method. The method used in the experiment is based on the Matlab Platform, FFT to realize the modeling of wave spectrum and Monte Carlo method, the analysis of the law of the sea surface shape changing with the wind field, etc. l, the random rough sea surface is modeled by Monte Carlo method, and the relationship between the wave spectrum and the random rough surface is analyzed. The simulation results show that: (1) in the modeling of rough surface with gauss type power spectrum, the variation of root mean square height and correlation length has a great effect on the fluctuation height and frequency of rough surface, the variation of the two parameters is the root mean square height and the correlation length, and when the correlation length is the same, the fluctuation of the rough surface will increase Based on the exponential power spectrum, when the root-mean-square height of one-dimensional random rough surface is fixed, the correlation length becomes smaller, then the rough surface transformation becomes more intense, and the changing period becomes smaller, it is concluded that the "vertical" variation characteristics are determined by the root mean square height and the "horizontal" variation characteristics are determined by the correlation length. (2) the results of Apel Spectra and Elfouhaily Spectra of rough sea surface simulated by different power spectra (Wave Spectra) of rough sea surface at different wind speeds of 5 m / s and 10 m / s show that the amplitude of fluctuation of the two spectra is larger when the wind speed is equal to 10 m / S, the fluctuation range of the Apel spectrum and the Elfouhaily spectrum increases with the increase of the wind speed. (3) with the increase of the wind speed, the simulated sea surface changes from gentle to undulating greatly, the theoretical values of the Apel spectrum and the Elfouhaily spectrum at different wind speeds of which shows that the random rough surface simulated by the power spectrum of the rough surface is consistent with the theoretical values.

KEYWORDS: Wave Spectrum; rough sea surface modeling; Monte Carlo Method; wind field variations

目录

第一章 绪论 1

1.1 研究背景与意义 1

1.2 国内外研究现状 1

1.3 研究内容 2

第二章 理论及实验方法 3

2.1 海浪谱模型 3

2.1.1 Apel谱 3

2.1.2 Elfouhaily谱 5

2.2 蒙特卡罗方法 8

2.2.1 一维粗糙面建模 8

2.2.2 二维粗糙面建模 9

第三章 粗糙面模拟及结果分析 10

3.1 一维粗糙面建模 10

3.1.1 基于高斯型功率谱的粗糙面 10

3.1.2 基于指数型功率谱的粗糙面 11

3.1.3 基于海浪谱的粗糙面 12

3.1.4 随机粗糙面与功率谱的验证 13

3.2 二维粗糙面建模 14

3.2.1 二维高斯型功率谱的粗糙面 14

3.2.2 二维指数型功率谱的粗糙面 15

3.2.3 二维海浪谱的粗糙面 16

第四章 结论及展望 18

参考文献 19

致 谢21

1. 绪论

1.1 研究背景与意义

对海浪的研究。在实验和理论上对真实海浪的研究启发人们对海浪进行建模的兴趣，利用的实验方法是在实验室通过利用风和造波机进行物理模拟实验，这种做法在一定条件下会被限制，便于海浪要素的测量和研究^[1]。在计算机模拟技术方面迎来了更好的效果，使得数值模拟海面取得了人们在做实验室时普及的应用；从宏观上看，海面是在大尺度、相似周期性的波浪上重复着小尺度的碎波浪^[2]。因此，人们常常从统计学的角度来研究海浪的各统计特征。其中，海浪谱模型是基于统计学的原理从能量角度刻画海面形状的一种有效方式，而海浪谱模型在海面过程中又是一个必需的输入量^[3]。因此，研究海面建模的关键。

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