In the k-epsilon model for turbulent boundary layers, the boundary values for 
k and epsilon are derived by balancing the production and dissipation terms 
in the equation for k using the log law. How do you derive them?

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Clarification of Question by sanjoser-ga on 18 Feb 2005 19:35 PST

I found a precise statement of me question as exercise 10.9 in the textbook 
"Turbulent Flows" by Stephen Pope. I would like an answer tothat exercise

Hi sanjoser!!


I found the answer to the exercise that you are requesting although I
cannot found an online the statement of 10.9 exercise, but you saw it,
didn't you?


The answer of the exercise 10.9 in the textbook "Turbulent Flows" by
Stephen Pope is in PDF format and I found it at the website of the
Sibley School of Mechanical and Aerospace Engineering, Cornell
University.


Note:
If you have Acrobat reader and/or GSVIEW skip the following part of the answer.
----------------------------------------------------------------
You will need Acrobat Reader to see it. You can download it from here:
http://www.adobe.com/products/acrobat/readstep2.html

The above download is a little heavy (20 MB) so if you prefer a small
download you can consider GSVIEW a a graphical interface for
Ghostscript:
First download the following files:
gs811w32.exe, AFPL Ghostscript 8.11 for Win32 (8 MB):
ftp://mirror.cs.wisc.edu/pub/mirrors/ghost/AFPL/gs811/gs811w32.exe

gsv46w32.exe, GSview 4.6 for Win32 (1.5 MB):
ftp://mirror.cs.wisc.edu/pub/mirrors/ghost/ghostgum/gsv46w32.exe

The instalation procedure is:
- Run the self extracted installer gs811w32.exe ti install Ghostscript
- Then run the GSview self extracting archive gsv46w32.exe
- Open the GSVIEW application and skip the register procedure if you
do not want to pay for the program. There is no requirement for you to
register GSview. According to the terms of the GSview licence, you can
use GSview without any payment.
- Click File menu --> Open and type the address of the PDF file (from
the net or your computer).
Note: You can also use this program to see Postscript files (.ps
files) that are very common in universities.
-------------------------------------------------------------

The address of the PDF document with the answer to the exercise 10.9
in the textbook "Turbulent Flows" by Stephen Pope is:
"Turbulent Flows - Stephen B. Pope - Cambridge University Press (2000)
- Solution to Exercise 10.9 - Prepared by: Zhuyin Ren - Date:
3/26/03":
http://eccentric.mae.cornell.edu/~mike/solutions/solutions/chapter10/10.9.pdf


You can also find many other answers to exercises of this textbook here:
"Exercise Solutions - Turbulent Flows":
http://eccentric.mae.cornell.edu/~mike/solutions/

You may be find useful the "S.B. Pope: TURBULENT FLOWS" page:
http://eccentric.mae.cornell.edu/~pope/TurbulentFlows.html

And the "Stephen B. Pope: Home Page":
http://eccentric.mae.cornell.edu/~pope/

----------------------------------------------------------

Search strategy:
"Turbulent Flows" Pope exercises
"exercise 10.9" Pope
Zhuyin Ren "turbulent flows"
Note that the results pages of the searches was not very useful to
find a direct link to the answer, but they lead me to the site of the
Sibley School of Mechanical and Aerospace Engineering  (the links are
almost dead probably due recent changes on the site structure). Then I
navigated the MAE site until I found the answer.


I hope that this helps you. Feel free to use the clarification feature
if you need some help with the required software or if some link does
not work or for any clarification that you need before rate this
answer.

Best regards.
livioflores-ga

PERFECT!!!! EXCELLENT!!!!
Exactly what I was looking for.

See the following document (only the cached version is free to access
it) and see if the answer to your question is there. I think that you
can find the article in a library:
"Modelling the Dynamics of Turbulent Floods" by Z. Mei, A. J. Roberts, Zhenquan Li:
http://66.102.7.104/search?q=cache:i_ZDUtPmRZEJ:epubs.siam.org/sam-bin/getfile/SIAP/articles/35886.pdf+%22turbulent+boundary%22&hl=en

The article appears in the SIAM Journal on Applied Mathematics Volume
63, Number 2, April, 2003.


Hope that this helps you.

I think this comment is a little advanced. My question is more on 
the level of an exercise, for example, in the textbook by Pope on
turbulent flows, which I'm trying to read. the production is given
as the turbulent viscosity times the derivative of the velocity squared, 
and using the log law to evaluate the derivative. I need some extra piece
of information to get a clear expression for k and epsilon. 
Does this comment help?