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Hi,

I was reading the manual on the sections of k-epsilon turbulence closure model and there are two options for: OPTION FOR THE BOUNDARY CONDITIONS OF K-EPSILON:
1 = No turbulence (k and ε takes the minimum values KMIN and EMIN defined in
subroutine CSTKEP), which is the default value,
• 2 = Hans and Burchard’s formula (introduced in version 7.0).

I was trying to find which formula is number 2 and I couldn't find it. There is also a reference to this matter this old post on the forum.

I think they are referencing to this paper but I'm not sure to which formula for both k and epsilon:
Umlauf, L., & Burchard, H. (2003). A generic length-scale equation for geophysical turbulence models. Journal of Marine Research, 61(2), 235-265.

On the file kepcl3.f, lines 255 for k and line 314 for epsilon, they name and show the formula but I don't understand all the variables that are in these equations.

Any help with this?

Thanks,
Cristian

Hello Cristian,

I am not sure the reference you gave is the right one. I will try to ask the person who introduced this boundary conditions in TELEMAC-3D.

Which variables do not you understand? I can try to explain from what I understand.

Chi-Tuan

PS: as you may have understood, "Hans and Burchard" is a mistake and should be read "Hans Burchard", I will change this in the manual.

Hi Chi-Tuan,

Thanks for your answer. In the file kepcl3, I found the following:and
Since this file use definitions from others files, I'm not sure about all the variables, that's why I don't fully understand the equations. For example, I know that

KBORL = K ON LATERAL SOLID BOUNDARIES
UETCAR = USTAR**2,
CMU = The constant for k-epsilon model (0.09D0, from CSTKEP.f)
KARMAN = KARMAN CONSTANT

But
DISTFOND I'm not sure. I can only assume is the distance to the bottom,
HAUT and Z0 I don't know.

Thanks for your help,
Cristian

Hello again Cristian,

Your first understanding is good.
DISTFOND is short for distance to the bottom in French (fond = bottom).
HAUT is water depth (hauteur = water depth in French).
Z0 is the friction coefficient. I assume this better works if using Nikuradse friction law.

Catherine told me the reference should be "Applied Turbulence Modelling in Marine Waters" book written by Hans Burchard, the reference for the GOTM model. I cannot check as I do not have it.

Her explanations:
At the bottom (i.e. inertial zone z < 0.2h): turbulence is at a local equilibrium, every variable is proportional to friction velocity:
- turbulent energy k = c u*2 with c an empirical constant around 3.3,
- Production = dissipation => eps = u*3/(Kz) with K = 0.4 (Karman constant).

Hope this helps,

Chi-Tuan

Thanks Chi-Tuan, as usual your answer are very useful.

One last question regarding the bottom stress. How should/can compute the bottom stress in Telemac3D?

According to the forum, in this topic, I can compute using the Telemac2D results file using:
VARIABLES FOR 2D GRAPHIC PRINTOUTS = 'US'
Is there a similar variable for the V component?
I hope my question make sense.

Best,
Cristian

Hello Cristian,

Variable US in VARIABLES FOR 2D GRAPHIC PRINTOUTS contains the magnitude of friction velocity, it is not a velocity component.

To compute the bottom stress, you can use the USER_PRERES_TELEMAC3D subroutine to implement the formula and, e.g. save it in one of the 4 arrays dedicated to users PRIVE1 to PRIVE4. It will enable you to visualise it at the end of the computation.

Hope this helps,

Chi-Tuan

To add to this, I usually calculate bottom shear stress in post-processing, for instance with a Calculator filter in ParaView, using the friction velocity. It's not the most elegant solution and it makes me wonder why friction velocity is the output instead of shear stress, but it works for me.

Also, if you are using GAIA, you can output shear stress directly, if I'm not mistaken.

Cheers,

André Renault