【正文】 畢 業(yè) 論 文（設(shè)計(jì)） 題 目： 海洋動(dòng)力學(xué)基本方程的研究 學(xué) 院： 數(shù)理與信息學(xué)院 專 業(yè)： 物理學(xué)（師范） 班 級(jí)： Ｂ１０物理 學(xué)生姓名： 盧小琴 學(xué) 號(hào)： 100603138 指導(dǎo)教師： 李鵬 2020 年 05 月 08 日 浙江海洋學(xué)院本科畢業(yè)論文 目錄 目錄 摘要 ................................................................. 1 ABSTRACT ............................................................. 2 前言 ................................................................................................................................... 3 1. 海洋動(dòng)力學(xué)基本方程的推導(dǎo) ...................................................................................... 5 壓力梯度項(xiàng)的導(dǎo)出 ............................................................................................ 5 質(zhì)點(diǎn)導(dǎo)數(shù)的導(dǎo)出 ................................................................................................ 5 NS 方程的導(dǎo)出 .................................................................................................. 6 連續(xù)方程的導(dǎo)出 .............................................................................................. 7 2. 有限差分法基本概念 .................................................................................................. 9 解域的離散化與差分網(wǎng)格的建立 ..................................................................... 9 微分方程的離散化 ........................................................................................... 10 階段誤差與相容性 .......................................................................................... 13 累積誤差與收斂性 .......................................................................................... 14 舍入誤差與穩(wěn)定性分析 .................................................................................. 16 3. 海浪表面線性波動(dòng) .................................................................................................... 17 海浪理論 ........................................................................................................... 17 表面二維線性波動(dòng)的基本方程與邊界條件 ................................................... 18 表面二維線性波動(dòng)的求解 ............................................................................... 21 結(jié)束語(yǔ) ............................................................................................................................. 25 參考文獻(xiàn) ......................................................................................................................... 26 文獻(xiàn)翻譯 ......................................................................................................................... 27 致謝 ................................................................................................................................. 37 浙江海洋學(xué)院本科畢業(yè)論文 摘要 1 海洋動(dòng)力學(xué)基本方程的研究 盧小琴 (浙 江海洋學(xué)院 數(shù)理與信息學(xué)院，浙江 舟山 316004) [摘 要 ]： 海洋 動(dòng)力學(xué)作為流體力學(xué)的一個(gè)分支，而流體力學(xué)作為宏觀力學(xué)的一個(gè)主要分支，它的成長(zhǎng)歷史悠久，是以理論研究比較成熟。作為最著名的流體控制方程，自然界中的各類流體都可以由納維一斯托克斯方程來(lái)模擬。長(zhǎng)期以來(lái)，在經(jīng)典流體動(dòng)力學(xué)中通常用修正過(guò)的NS方程 組 描述海洋運(yùn)動(dòng)。 本文 的目的就是為了幫助對(duì) NS方程有興趣的讀者 掌握海洋動(dòng)力學(xué)基本方程的物理意義和數(shù)學(xué)推導(dǎo) ，希望在此基礎(chǔ)上能夠建立一個(gè)最簡(jiǎn)單的物理模型，進(jìn)行求解，來(lái)把握最主要的物理內(nèi)涵和規(guī) 律。本文 著重 介紹了 NS方程的推導(dǎo)過(guò)程，及求解 NS方程的數(shù)值方法中有限差 分法的 差分格式 的建立 及其誤差和基本性質(zhì)的分析， 如相容性、收斂性、穩(wěn)定性分析等，能讓讀者更加清晰的了解 NS方程的求解方法。最后，本文用 NS方程研究理想的規(guī)則波動(dòng)（正弦波和斯托克斯波等），視海水不可壓且運(yùn)動(dòng)無(wú)旋，以此說(shuō)明實(shí)際海洋中發(fā)生的一些比較規(guī)則的波動(dòng)現(xiàn)象。 本文 具體推導(dǎo)了海洋動(dòng)力學(xué)基本方程，推導(dǎo)出由 三個(gè)運(yùn)動(dòng)方程和一個(gè)連續(xù)方程構(gòu)成的 NS方程組，并由此推出海浪 表面二維線性波動(dòng)的基本方程。 對(duì)于無(wú)旋運(yùn)動(dòng)，分開求解運(yùn)動(dòng)學(xué)問(wèn)題和動(dòng)力學(xué)問(wèn)題， 即先從拉普拉斯方程和邊界條件求得速度（或求得勢(shì)函數(shù)），再由拉格朗日積分求得壓強(qiáng)，使問(wèn)題全部解決。 [關(guān)鍵詞 ]:海洋動(dòng)力學(xué)； NS 方程； 有限差分方法； 二維線性波動(dòng) 浙江海洋學(xué)院本科畢業(yè)論文 ABSTRACT 2 THE BASIC EQUATIONS OF OCEAN DYNAMICS RESEARCH Lu Xiaoqin (School of Mathematics, Physics amp。Information Science, Zhejiang Ocean University Zhou Shan， 316004) Abstract： Ocean dynamics is a branch of fluid mechanics, and fluid mechanics is a major branch of the macroscopical mechanics. It has a long history, so the theoretical studies are relatively mature. NavierStokes equations of fluid control as the most famous equation can be used to simulate various types of fluid in nature. For a long time, in the classical fluid dynamics, we usually use the NS equations to describe the marine sports. The purpose of this paper is to help the readers who are interested in the NS equations to grasp the physical meaning of the basic equations of ocean dynamics and mathematical derivation. On this basis, we hope to build a simple physical model for solving the equations, and grasping the meaning of the most important physical and laws. This paper describes the derivation of NS equations and numerical methods for solving NS equations to establish its basic properties in the difference schemes of finite difference method , such as patibility, convergence and stability. Then, this paper allows readers to more clearly understand the method for solving NS , we study the ideal equation rules fluctuations (sine and Stokes, etc.) with NS equations, depending on the water and inpressible irrotational motion. It can be an example of some of the more regular wave phenomena occurring in the actual ocean. In this paper, we definitely derived basic equations of ocean dynamics, and derived the NS equations which are posed of three equations of motion and a continuity equation。 And thus derived a two dimensional surface waves basic equations of linear fluctuations. For irrotational motion, kinematics solve separate problems and dynamics that start with the Laplace equations and boundary conditions to obtain the speed (or seek potential function). Then the pressure is obtained by the Lagrange points, so that all the problems resolved. Key Words: ocean dynamics； NS equations； finite difference method； two dimensional linear fluctuations