A Mathematical Introduction to Fluid Mechanics (Texts in Applied Mathematics, 4) 3rd Edition by Alexandre J. Chorin (PDF)

Description

A presentation of some of the basic ideas of fluid mechanics in a mathematically attractive manner. The text illustrates the physical background and motivation for some constructions used in recent mathematical and numerical work on the Navier- Stokes equations and on hyperbolic systems, so as to interest students in this at once beautiful and difficult subject. This third edition incorporates a number of updates and revisions, while retaining the spirit and scope of the original book.

User’s Reviews

Editorial Reviews: Review From the reviews:”… The book contains some of the basic ideas of fluid mechanics in a mathematically attractive manner…has the very advantage of providing the solution of the differential equations using the new and modern techniques…the material is very well presented both the mathematical arguments as well as the physical input.” Physicalia

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book is excellent for a mathematician or a engineering student with good math basis. You do not need to know a lot of advance math in order to follow the book. However I think more formalism should be included in some essential parts of the book and it also should include a few more examples.

⭐This book looks like it was written with a typewriter. The text is very light and sometimes hard to read.

⭐The presentation is needlessly confusing, and feels more like abridged class notes than a proper and rigorous introduction. Overall, the subject is presented starting from the specific to the general case ( viscous flow ), which doesn’t help here. Also, the lack of tensor notation is detrimental ( especially when talking about tensors! ).For those looking for a proper mathematical approach to fluid mechanics, I would recommend instead Rutherford Aris’ “Vectors, Tensors and the Basic Equations of Fluid Mechanics”. Night and Day! For instance, Aris’s introduction of Lagrangian and Eulerian viewpoints along with the material derivative is exemplary in its clarity. Aris’ book also has the advantage of tending to introduce the general equations first, and trimming them down for specific cases, which helps a lot. Why learn the simplified equations, when it is not the full story? For example, Cauchy’s equation of motion is given with the divergence of the stress tensor from the start — and is always true –, rather than the gradient of pressure, which is a sub-case pertaining to non-viscous flow.

⭐I would agree with the first reviewer’s comments that this is an excellent book for someone with a strong advanced math background. It is a very concise mathematical treatment of fluid mechanics. I can also see why the 2nd reviewer had some issues. I would not recommend this book for an undergrad class as it does not have very strong verbal descriptions of the mathematical formulas which would make understanding somewhat difficult to the non-mathematician, but I would not trust his judgment on accuracy. This book is very good for the graduate engineer that wants to challenge his understanding of fluid mechanics to a more mathematical understanding. If you are not confident in your math skills however, you may want to look elsewhere.

⭐A very interesting book by Chorin and Marsden, In many ways very original in its study of fluid mechanics. Fluids are studied in a mathematical manner so that much that remains uninvestigated in standard fluids texts is revealed here. A typical example is the local decomposition of a velocity vector described in terms of the deformation tensor at an early stage in the book and is closely related to the well known Helmholtz decomposition. In fact, while the Helmholtz decomposition is well known and commonly used in, for example the projection method, its proof relies very much on assuming the decomposition to be true and then “proved”, firstly in proving orthogonality and then existence. However, there seems to be a lack in showing how this decomposition comes about and the earlier local decomposition gives a hint in this direction by showing how deformation is related to a div-free vector and how a curl-free vector is related to volume conservation. Finally, how a harmonic field is akin to a translation. In addition, Chorin expresses how the existence of a vortex sheet at solid wall boundaries gives rise to a potential flow field almost everywhere except within a boundary layer at the wall diffused into the domain through vortex diffusion. This is the first time I have seen such a view. Naturally it is this which led Chorin to define the well known vortex method in CFD.A good addition to the fluid dynamics library.

⭐The problem is not with the text itself, is with the book’s quality; in particular, with the images. They are of the worst quality possible, many details are lost in this version. The paper is also of a very bad quality that has nothing to do with the old Springer books. If you compare the images from the book with those of the ebook, you can tell they use the chipper materials available. One could print a better book with a regular printer.I wouldn’t recommend these print on demand Springer books, specially the ones printed by Amazon. They are extremely expensive for what you get.

⭐die noch mit Schreibmaschine geschrieben wurde, habe ich dieses Buch verfolgt. Alexandre Chorin und Jerry Marsden sind zwei große Namen in der Angewandten Mathematik und das vorliegende Buch erfüllt den Anspruch im Titel voll und ganz. Die Autoren sind um rigorose Beweise bemüht und es gelingt ihnen damit der Nachweis, dass Strömungsmechanik eigentlich ein Teil der Mathematik ist. Wer einen Überblick über die theoretische Seite der Strömungsmechanik sucht, ist mit diesem Buch hervorragend bedient.

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⭐JUSTO LO QUE BUSCABA

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