克洛德-路易·纳维Claude-Louis Navier

克洛德-路易·纳维的父亲是一名律师，在法国大革命期间是巴黎国民议会的成员。然而，纳维的父亲于1793年去世，当时纳维只有八岁。此时全家住在巴黎，但在纳维的父亲去世后，他的母亲回到了她的家乡索恩河畔沙隆，将纳维留在巴黎，由她的叔叔埃米兰·戈泰照顾。

Emiland Gauthey 是一名土木工程师，在巴黎的桥梁与道路工程队工作。他被认为是法国顶尖的土木工程师，无疑使纳维对工程学产生了兴趣。尽管鼓励纳维进入巴黎综合理工学院，Gauthey 在教导纳维方面似乎并不那么成功，后者可能只是一个晚熟者，因为他在1802年才勉强考入巴黎综合理工学院。然而，从入学时几乎垫底的成绩开始，纳维在巴黎综合理工学院的第一年取得了如此大的进步，以至于在年末成为前十名学生之一，并在第二年被选中参加布洛涅的特别野外工作。

在巴黎综合理工学院的这第一年里，纳维由约瑟夫·傅里叶教授分析，后者对这位年轻人产生了显著的影响。约瑟夫·傅里叶成为纳维的终身朋友，同时也是他的老师，并且从那时起就对纳维的职业生涯产生了积极的兴趣。1804年，纳维进入桥梁公路学校，两年后作为该校最优秀的学生之一毕业。纳维毕业不久后，他的叔祖父Emiland Gauthey去世，而已经离开巴黎从事野外工作的纳维应桥梁公路工程团的要求返回巴黎，承担起编辑Gauthey著作的任务。奥斯卡·安德尔森在[3]中写道：-

在接下来的13年里，纳维被公认为工程科学学者。他编辑了他叔祖父的著作，这些著作代表了土木工程众多应用中的传统经验方法。在这一过程中，基于他自己在理论力学方面的研究，纳维为Gauthey的著作增添了一些分析的色彩。这一点，结合纳维为执业工程师编写的教科书，将工程科学的基本原理引入了一个此前几乎完全依赖经验的领域。

纳维于1819年负责桥梁公路学校的应用力学课程，并于1830年被任命为该校教授。他不仅仅延续学校的传统教学，而是改变了教学大纲，更加注重物理学和数学分析。此外，他从1831年起接替奥古斯丁·路易·柯西担任巴黎综合理工学院的教授。然而，他的教学理念并非所有人都认同，在他被任命为巴黎综合理工学院教授后不久，纳维就因约瑟夫·傅里叶的热理论教学问题与西莫恩·德尼·泊松发生了争执。

作为道路与桥梁建筑专家，他第一个发展了悬索桥理论，在此之前悬索桥都是按经验原则建造的。然而，他在塞纳河上建造悬索桥的重大项目最终以失败告终。项目遇到困难的真正原因是市议会从未支持过它。尽管如此，工程还是继续进行，但当桥几乎完工时，一端的下水道破裂，导致桥的一个支座移动。桥梁与道路工程队认为这不是大问题，报告说修复很简单，但市议会正在寻找借口停止项目，于是他们将桥拆除了。

今天人们记住纳维，不是因为他当年作为著名桥梁建造者的名声，而是因为流体动力学中的纳维-乔治·加布里埃尔·斯托克斯方程。他研究工程、弹性和流体力学等应用数学课题，此外还对Fourier series及其在物理问题中的应用做出了贡献。他于1821年给出了著名的不可压缩流体的纳维-乔治·加布里埃尔·斯托克斯方程，1822年又给出了粘性流体的方程。

然而，我们应该注意到，尽管纳维并未完全理解他所建模情况的物理学，他还是推导出了纳维-乔治·加布里埃尔·斯托克斯方程。他不理解流体中的剪应力，而是基于修改莱昂哈德·欧拉的方程以考虑流体中分子之间的力来开展他的工作。尽管他的推理在今天看来是不可接受的，正如安德尔森在[3]中写道：-

具有讽刺意味的是，尽管纳维对剪应力没有概念，也没有打算获得描述涉及摩擦的运动的方程，但他还是得出了这类方程的正确形式。

纳维获得了许多荣誉，其中也许最重要的是1824年当选为巴黎的Académie des Sciences。他于1831年成为荣誉军团骑士。

最后，我们应该稍微谈谈纳维的政治立场。当然，他经历了一个整个欧洲，尤其是法国，政治运动风起云涌的时期。对纳维政治思想影响最大的两个人是Auguste Comte——被誉为社会学和实证主义创始人的法国哲学家，以及Henri de Saint-Simon——他发起了圣西门主义运动，提出了一种基于社会利用科学技术的社会主义意识形态。

Comte曾在巴黎综合理工学院接受教育，1814年入学，在那里学习数学。纳维任命他为巴黎综合理工学院的助手之一，这一联系使纳维成为Comte和Saint-Simon思想的热情支持者。纳维相信一个工业化的世界，在那里科学和技术将解决大部分问题。他还反对战争，反对法国大革命的流血和拿破仑的军事侵略。

从1830年起，纳维受雇于政府担任顾问，就如何利用科学技术改善国家提供建议。他就道路运输政策、公路和铁路的建设提出建议。他的许多报告既显示了他作为工程师的卓越才能，也显示了他对建设一个惠及所有人的工业化社会的强烈政治观点。

Claude-Louis Navier's father was a lawyer who was a member of the National Assembly in Paris during the time of the French Revolution. However Navier's father died in 1793 when Navier was only eight years old. At this time the family were living in Paris but after Navier's father died, his mother returned to her home town of Chalon-sur-Saône and left Navier in Paris to be cared for by her uncle Emiland Gauthey.

Emiland Gauthey was a civil engineer who worked at the Corps des Ponts et Chaussées in Paris. He was considered the leading civil engineer in France and he certainly gave Navier an interest in engineering. Despite encouraging Navier to enter the École Polytechnique, Gauthey seems not to have been that successful in teaching Navier, who may just have been a late developer, for he only just scraped into to École Polytechnique in 1802. However, from almost bottom place on entry, Navier made such progress in his first year at the École Polytechnique that he was one of the top ten students at the end of the year and chosen for special field work in Boulogne in his second year.

During this first year at the École Polytechnique, Navier was taught analysis by Fourier who had a remarkable influence on the young man. Fourier became a life-long friend of Navier as well as his teacher, and he took an active interest in Navier's career from that time on. In 1804 Navier entered the École des Ponts et Chaussées and graduated as one of the top students in the school two years later. It was not long after Navier's graduation that his granduncle Emiland Gauthey died and Navier, who had left Paris to undertake field work, returned to Paris, at the request of the Corps des Ponts et Chaussées, to take on the task of editing Gauthey's works. Anderson writes in [3]:-

Over the next 13 years, Navier became recognised as a scholar of engineering science. He edited the works of his granduncle, which represented the traditional empirical approach to numerous applications in civil engineering. In that process, on the basis of his own research in theoretical mechanics, Navier added a somewhat analytical flavour to the works of Gauthey. That, in combination with textbooks that Navier wrote for practicing engineers, introduced the basic principles of engineering science to a field that previously had been almost completely empirical.

Navier took charge of the applied mechanics courses at the École des Ponts et Chaussées in 1819, being named as professor there in 1830. He did not just carry on the traditional teaching in the school, but rather he changed the syllabus to put much more emphasis on physics and on mathematical analysis. In addition, he replaced Cauchy as professor at the École Polytechnique from 1831. His ideas for teaching were not shared by all, however, and soon after his appointment to the professorship at the École Polytechnique Navier became involved in a dispute with Poisson over the teaching of Fourier's theory of heat.

A specialist in road and bridge building, he was the first to develop a theory of suspension bridges which before then had been built to empirical principles. His major project to build a suspension bridge over the Seine was, however, to end in failure. The real reason that the project ran into difficulties was that the Municipal Council never supported it. Despite this it went ahead but, when the bridge was almost complete, a sewer ruptured at one end causing a movement of one of the bridge supports. The problem was not considered a major one by the Corps des Ponts et Chaussées who reported that repairs were straightforward, but the Municipal Council were looking for an excuse to stop the project and they had the bridge dismantled.

Navier is remembered today, not as the famous builder of bridges for which he was known in his own day, but rather for the Navier-Stokes equations of fluid dynamics. He worked on applied mathematics topics such as engineering, elasticity and fluid mechanics and, in addition, he made contributions to Fourier series and their application to physical problems. He gave the well known Navier-Stokes equations for an incompressible fluid in 1821 while in 1822 he gave equations for viscous fluids.

We should note, however, that Navier derived the Navier-Stokes equations despite not fully understanding the physics of the situation which he was modelling. He did not understand about shear stress in a fluid, but rather he based his work on modifying Euler's equations to take into account forces between the molecules in the fluid. Although his reasoning is unacceptable today, as Anderson writes in [3]:-

The irony is that although Navier had no conception of shear stress and did not set out to obtain equations that would describe motion involving friction, he nevertheless arrived at the proper form for such equations.

Navier received many honours, perhaps the most important of which was election to the Académie des Sciences in Paris in 1824. He became Chevalier of the Legion of Honour in 1831.

Finally we should say a little of Navier's political position. Of course he lived through a period when there was great political movements throughout Europe and in France in particular. The two men who had the most influence on Navier's political thinking were Auguste Comte, the French philosopher known as the founder of sociology and of positivism, and Henri de Saint-Simon who started the Saint-Simonian movement which proposed a socialist ideology based on society taking advantage of science and technology.

Comte had been educated at the École Polytechnique, entering in 1814, where he had studied mathematics. Navier appointed him as one of his assistants at the École Polytechnique and this connection was to see Navier become an ardent supporter of the ideas of Comte and Saint-Simon. Navier believed in an industrialised world in which science and technology would solve most of the problems. He also took a stand against war and against the bloodletting of the French Revolution and the military aggression of Napoleon.

From 1830 Navier was employed as a consultant by the government to advise on how science and technology could be used to better the country. He advised on policies of road transport, the construction of both roads and railways. His many reports show both his remarkable abilities as an engineer coupled with his strong political views on building an industrialised society for the advantage of all.