Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

  Boundary layer theory in fluids learning resources

+ 6 like - 0 dislike
1417 views

I'm trying to understand boundary layer theory in fluids. All I've found are dimensional arguments, order of magnitude arguments, etc... What I'm looking for is more mathematically sound arguments. Not rigorous as in keeping track of all epsilons and deltas, but more rigorous than an heuristic argument. Hope you understand what I mean. Some free resources available on the web would be preferred, but if you can suggest book titles that's also helpful. Thanks.

Edit: The applications I have in mind are the calculation of damping in surface waves in basins of various shapes (circular, rectangular, etc).


This post imported from StackExchange Physics at 2014-04-30 05:30 (UCT), posted by SE-user becko

asked May 13, 2011 in Resources and References by PKM2 (0 points) [ revision history ]
recategorized Apr 30, 2014 by dimension10

3 Answers

+ 3 like - 0 dislike

Boundary layer theory come in as a method to "simplify" the mathematics in fluid mechanics, so that it is solvable analytically. It separates the fluid as two regions:

  1. where the viscosity effect is important, i.e. boundary layer
  2. where viscosity is not important

This approach has been proven useful for large range of applications, that's why aerodynamics (for example) has flourished and matured a lot in the past century. In some cases where Navier-Stokes has an exact solution, researcher had shown that there exist a boundary layer where viscosity is important, and outer region where it is negligible. These examples are abundant in Fluid Mechanics book, such as Kundu-Cohen's, or Landau-Lifshitz's. By the nature of this theory, it would be interesting if there are rigorous expositions mathematically as you may probably want to see. However, if Landau's treatment did not satisfy you, you may want to check a book by Oleinik and Samokhin titled Mathematical Models in Boundary Layer Theory.

A probably important thing to note, boundary layer approximation may cause erroneous result due to the assumption of the thin boundary layer is not satisfied. Such an example (quite recent) can be seen in an article by Doinikov and Bouakaz in JASA: http://asadl.org/jasa/resource/1/jasman/v127/i2/p703_s1?isAuthorized=no

This post imported from StackExchange Physics at 2014-04-30 05:30 (UCT), posted by SE-user bowo
answered Oct 31, 2012 by bowo (0 points) [ no revision ]
+ 1 like - 0 dislike

I will probably disappoint you now, but fluid dynamics must be approximative. You start from a model which is (to some extent) rigorous and intuitive and consists of partial differential equations - Navier-Stokes equations, continuity equation and Fourier-Kirchhoff (if heat transfer is involved) - with proper boundary conditions. However, for most of the shapes, there are no analytical solutions. Therefore, we first throw out unimportant information and make the parameters somehow independent. The standard dimensionless numbers (Re, Sc, Eu ...) are often used (because we are used to them and history proved they are most useful). The "boundary values" or "magnitude arguments" (e.g. Re>10000) are usually stated in books very approximative but model-independent. If you want more exact results, you need to numerically solve the partial differential equations (there are very user-friendly packages for this, e.g. COMSOL Multiphysics...). For some models, you can very precisely calculate e.g. heat transfer coefficient. At very high Re/Pr... you will observe those approximate model-independent trends.

This post imported from StackExchange Physics at 2014-04-30 05:30 (UCT), posted by SE-user Boris
answered Apr 10, 2012 by Boris (0 points) [ no revision ]
+ 0 like - 0 dislike

I learnt boundary layer theory from Bender-Orszag, and found it fairly simple, though it gets a little more mathematically involved than I'd hope. Here's the book on google books.

I also wrote some notes about them in a course on numerical methods I took a year ago, which you could find useful if you speak Italian.

This post imported from StackExchange Physics at 2014-04-30 05:30 (UCT), posted by SE-user Ferdinando Randisi
answered Oct 31, 2012 by Ferdinando Randisi (0 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOverfl$\varnothing$w
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...