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I am interested in getting a good introductory book to fluid dynamics. I am a first year PhD student in Mathematics.

My project involves a simplification of the Navier-Stokes equations. But I don't have any background whatsoever on fluid dynamics or physics for the matter (at least beyond high school level).

Thank you for any recommendations! Please don't just post random books you found on Amazon (I can do that myself). I am interested in the opinion of people who have done some fluid dynamics, the more the better, and know about the field.

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"An Introduction to Fluid Dynamics" by G. K. Batchelor is a classic and is considered as the Bhagavad Gita of fluid dynamics. I have read this book as an undergrad and hence the knowledge required is just high school mathematics and physics.

Recent texts, in my opinion, are unfortunately biased too much towards computational fluid dynamics, than explaining the mathematical and physical underpinning of the fluid dynamics.

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Besides Batchelor, A Mathematical Introduction to Fluid Mechanics by Chorin and Marsden is very good and concise. I think it's well suited for a math student, as opposed to most books which have a more engineering flavor.

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You've probably found the books you need now. Anyhow 'The Introduction to computational fluid dynamics' by Versteeg is very good.

http://www.scribd.com/doc/7504135/An-Introduction-to-Computational-Fluid-Dynamics-Versteeg

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    $\begingroup$ The person who asked the question needs info on Navier Stokes equations! Hence this books is very appropriate as the introductory chapters in particular explain the physics along with the equations! $\endgroup$ – Hooman Jul 2 '12 at 21:52
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    $\begingroup$ Marvis, I believe that a course/reading on NS equations, which is a really applied math topic, should be followed/integrated by a topic on CFD. You learn a lot on NS equations by looking at the challenges and difficulties of its discretization schemes. $\endgroup$ – bartgol Dec 3 '12 at 7:18
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I have enjoyed the following books: Elementary Fluid Dynamics by Acheson. The book by Kundu and Cohen, Fluid Dynamics is also extremely enjoyable. Besides, I have found the following lecture notes useful:

Paul Fife, A Gentle Introduction to the Physics and Mathematics of Fluid Flow:

http://www.math.utah.edu/~fife/gentleb.pdf

Simon Malham, Introductory Fluid Mechanics:

http://www.ma.hw.ac.uk/~simonm/fluidsnotes.pdf

At a little higher level are these notes by Vladimir Sverak:

http://www.math.umn.edu/~sverak/course-notes2011.pdf

and the book by Majda and Bertozzi: Vorticity and Incompressible flow.

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Dont ignore the CFD-oriented books. Good ones such as Godlewski and Raviart "Numerical approximation of hyperbolic systems of conservation laws" rely on solid theoretical underpinning. Another addition to your list might be M. J. Lighthill "An informal introduction to theoretical fluid dynamics". Be aware that there are surprisingly large differences between compressible and incompressible flow. They sometimes look like almost different subjects.

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