Wilhelm Oseen's Preface to Hydrodynamics

In 1927 Wilhelm Oseen published the book Neuere Methoden Und Ergebnisse In Der Hydrodynamik. We give below a modified version of a short extract from the Preface to that book.

Baruch Spinoza wrote to Henry Oldenburg concerning Robert Boyle"s first scientific publication, New Experiments Physico-Mechanicall, Touching the Spring of the Air and Its Effects (1660). His letter includes the following passage: "Finally, notice this on the side, it is sufficient for general understanding the nature of liquids, knowing that one can move one's hand in a liquid with a movement proportional to it in all directions without resistance, which is well known to those who pay close attention to those terms that explain nature as it is in itself, instead of their relationship to human sensory perception, but I do not think this description is worthless, on the contrary, I would consider an equally accurate and faithful description of each fluid to be extremely useful in understanding its peculiarity, which is what most philosophers strive for."

The property of the "ideal" fluids of not resisting a body during stationary movement, which Spinoza mentions here (1662?), was called "the paradox of d'Alembert" or "the paradox of Euler" in the eighteenth century.

The motivation for the author's investigations, on which this book reports, was the desire to shed light on this paradox by studying the movements of real, viscous liquids. At the time these studies were started, the theory of partial differential equations was a popular subject of mathematical research. It seemed to me a tempting task to use the methods gained in this part of pure mathematics to solve that riddle.

In order to gain a basis for the following investigations, I first had to examine the linear systems of partial differential equations, which can be obtained from the equations of motion of a viscous liquid by omitting the quadratic terms. I had to determine the basic solutions for those systems. The first part of this book reports on these investigations.

The above-mentioned linear systems of partial differential equations, which can be obtained from the complete hydrodynamic differential equations by omitting the quadratic terms, apply approximately to slow movements of a viscous liquid. Colloid chemistry has given this area of slow motion scientific importance. My preoccupation with the subject gave me the solution to a hydrodynamic puzzle in this area, the Whitehead paradox. Lamb showed that another hydrodynamic puzzle, the Stokes paradox, can also be solved by my methods. Following my work, faxing has promoted the theory of slow fluid movement through extensive and valuable research. I hope that the compilation of the results obtained in this field in the last few years, which I give in the second part of my book, will be welcome for colloid chemistry.

The main goal of my investigations was, however, to carry out the crossing of the viscous toughness in an exact manner. I have not yet achieved this goal. On the other hand, I was able to cross the border in the linear systems I mentioned above. The results I got are in sharp contradiction to the theory of ideal liquids, but in qualitative agreement with the behaviour of the real liquids. From these facts it seemed to me that the d'Alembert paradox is based on poorly executed border crossings with a tenacity that is vanishing. The studies by Zeilon, who continued my work in this area, have shown that my border crossing gives far more than this negative result. In terms of resistance, it does not give exact values, but it does give correct values in terms of magnitude. And from the pressure distribution on the front of a body, it gives an almost correct picture, also quantitatively. The third part of the book reports on these things.

Last Updated April 2020