Need feedback for a new book in fluid mechanics
 

Do you have topics about fluid mechanics in mind that you needed some information about during your research but couldn't find enough references?

My colleague and I are collecting ideas for writing a general book on fluid dynamics and turbulence. Novelty is a key and that's why I need to know which topics are considered "hot" and on which there is lack of information in the text books, in the area of fluid mechanics.

Hi
 

To the best of m knowledge the best book is "Turbulent flow" of Stephen B. Pope.

There are a lot of concepts in compressible turbulence that just don't have textbook definitions or constructions. Off the top of my head, dilatational and solenoidal modes/waves come up a lot in the literature, but I only ever found them discussed in one book. Maybe there's some fantastic compressible turbulence textbook out there, but not in my university's library. Gatski's book is pretty good.

Attention needs to be given to the validity of the Boussinesq hypothesis, which is the basis of all eddy-viscosity turbulence models. There is an increasing amount of numerical and experimental evidence that it is not universally valid.

I think a lot more attention needs to be paid to Fourier analysis in general than what I have seen in textbooks. IMHO the spectral paradigm is far more critical to understanding modern turbulence theory than the statistical moment paradigm. Moments just don't give you a dynamic view of things. Things like understanding a filter in terms of its transfer function, what artificial dissipation means in Fourier space, what Gibbs phenomena is from a Fourier POV, understanding backscatter as a phenomenon arising from nonlinear interactions by looking at the NSEs in a Galerkin expansion, etc, have all proven critical to me so far and weren't discussed much in the textbooks I used for my graduate courses.

If you want something really, really novel for incompressible flow, look at "A Hermite finite element method for incompressible fluid flow", IJNMF 64:376-408 (2010), "Computation of incompressible thermal flows using Hermite elements",CMAME 199:3297-3304 (2010), "A velocity-stream function method for three-dimensional fluid flow", CMAME 209-212:66-73 (2012). These implement the missing velocity-stream function method from the triad: stream function, velocity & vorticity.

Josh, thanks for the detailed comments. I agree with you on the point on Boussinesq approximation. I would also question the generality of log-law. And maybe expand some statistical approach to turbulence ... I'd like focusing on incompressible flows though.

Good points! need to read about them. Thanks.

Thanks Hasan, but I wanted to know if there are topics that you think are missing in such textbooks as Pope's.

I'm an undergrad and there is a lot of discussion in literature about vortices, but I've never seen a nice, clear textbook explanation at the undergrad level of what they actually are, their characteristics and what the effects of vorticity are. Perhaps I'm not looking in the right places, but it's often just assumed that you know qualitatively what a vortex is, my understanding is that it is just an area of rotation in fluid but I have no idea if this is a good definition or not.

Right, But you might want to try "vorticity and vortex dynamics" of Jie-Zhi Wu, Hui-Yang Ma, Ming-De Zhou.