open TELEMAC-MASCARET The mathematically superior suite of solvers

Dear Turbulence Experts,

I have some questions about the computation of the turbulent diffusion with the mixing length model. It is the first time I looked in detail into the turbulence models of TELEMAC2D, so I do not have the big picture in mind.

The parameter LMB describes a length which is the minimum of the distance to the nearest wall (MESH%DISBOR%R(K)) an the water depth times a calibration coefficient MIXING(1)*HC.

When I understand it correct, the current implementation regards only for boundary elements the distance to the nearest wall. Is this because it is assumed that the water MIXING(1)*HC is in most cases smaller than the distance y, or is it because the implementation of the distance to the nearest boundary is to complicate? I'm not an expert about turbulence modeling, maybe this length should only be regarded for boundary elements?

For me it looks like the model can be very useful for well defined geometries where no wetting/drying of elements occur, e.g. flumes. But when it comes to applications where one simulate the flow in a river it is not clear if a dry element may also acts like a wall?

Further I guess that a single choice for the calibration parameter MIXING(1) will be only meaningful for small domains?


Best regards,

Leo

Hi Leo,

I don't consider me as turbulence expert but some tentative answers:
Yes, lets say in prototype scale, at the outer boundary the MIXING(1)*HC in most cases will be smaller than the distance y. However, at inner boundaries the distance may be the length scale. The approach implemented in this way damps somwhat the turbulence production at the boundaries.

But you are right: the correct approach would be to check the closest distance to the wall for all the nodes and do the test for all the nodes!

When I implemented the model I didn't spend a lot of time on this since in the practice probably you don't gain any improvements. Furthermore, most of the 2D turbulence models implemented in some codes even don't have any limiter treatment for the wall nodes. In my view 2D turbulence is never a clean thing.. consider for example also the whole dispersion issue.

I don't think that wetting/drying is an issue for the turbulence model. First of all, the water depth goes to zero which reduces the turbulent viscosity (both components of viscosity) and second, in shallow areas or near-dry zones usually the depth-averaged velocity gradients are very low or vanish which implies that the horizontal turbulence production goes to zero.

I don't think that the size of the domain plays a role for the calibration parameter MIXING(1). The calibration coefficients in the sub-routine account for turbulent diffusion only, and are derived based on super-duper assumptions of flow behaviour (perfect logarithmic profile, only 2D flow (x-z), etc.). To account for dispersion in 2D, e.g. due to non-uniformity of vertical velocity gradients, one should increase these coefficients. Often ALPHA in the depth-averaged parabolic model is set to 0.5. For the coefficient MIXING(1) in the Mixing Length model there is not much literature out there. Stansby for example proposed the horizontal mixing length to be a multiple of 6 of the vertical mixing length which means the mixing length is approximately half the water depth or MIXING(1)=1.25

Enclosed also my paper for TUC 2016. By the way, where are the proceedings from TUC 2016?

Best regards,
Clemens

Hi Clemens,

thank you for your answer and the TUC Paper, now understand the ideas and the implementation in Telemac and the choice of the parameter MIXING(1) .
I've also looked in the paper of Wu et al. , they had only small differences in the velocity profiles for the investigated turbulence models for the river examples.

My question about wetting and drying came up because I thought that a dry element may act like a wall if the bottom gradients are large.

I fully agree, turbulence modeling looks never like a clean thing. One need also velocity gradients/derivatives which can be tricky to approximate.


Best regards,

Leo