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Hi all,

I want to model friction at the free surface in a 3D model. I have implemented the friction at free surface as a source term in subroutine source.f using a classical quadratic friction law based on an equivalent sand roughness coefficient with the following expression:

S = 0.5 * 2 * (Karman / LN(30*dz/ks))**2 * Velocity

With dz = distance between the two upper planes and ks = 0,01 m. S is applied to the surface nodes only.

I made tests in a rectangular channel (100 m long, 20 m wide) with flat bottom, water depth of 5 m and current speed of 0,05 m/s. I used 10 evenly distributed vertical planes, k-epsilon and non-hydrostatic version. Tests were performed with and without bottom friction.

For the test without bottom friction, we can see the effect of surface friction with a surface current progressively decreasing from 0,05 to 0,04 m/s in the downstream direction whereas the current at the bottom is logically equal to 0,05 m/s (no friction). See below.



But if I use bottom friction (tested with ks = 0,16 m, coresponding to a Strickler of 35 for 5 m depth), the surface current is not reduced, staying at the mean value of 0,05 m/s, see below.



If I reduce ks at the bottom to 0,01 m, we can see that the surface current is somewhat reduced in the upstream part but not downstream, see below.



I would have expected the surface current not to be influenced by the bottom friction. Why do I observe this?

I made another test when I increase the current speed to 1 m/s (same water depth and with bottom friction on, ks bottom = 0,16 m). In that case the surface current is indeed lowered due to the higher velocity (friction = a x V**2).



Does someone have any input on why the effect of surface friction is reduced when accounting for bottom friction compared to the case without bottom friction?

Any help is greatly appreciated!

Thanks in advance,

Best regards
PL

PS: on all of the above pictures, the current direction is from left to right.

Hello,

I would say that what you find is rather logical. If the total discharge is constant, adding friction on the bottom will increase the velocity elsewhere, so it may cancel the friction effect at the free surface. However it is true that we expect to see a maximum in between. What happens if you put the same friction at the bottom and at the free surface? We should find some symmetry and a maximum of velocity at mid-depth... unless the slope at the free surface has some influence on the result, in which case we should get more symmetry with a smaller friction giving a smaller slope.

Well this is not an answer but just some hints to understand what happens...

With best regards,

Jean-Michel Hervouet

Hello,

Thank you for your reply!
Yes, I made the test with symmetrical friction, see the third image in the first post, there is both ks = 0,01 m at the bottom (with LAW OF BOTTOM FRICTION =5) and in the source term at the free surface. And we do not get any symmetrical profile - at best, there is a slight decrease of the surface velocity (order of magnitude 0,001 m/s). That was the test that triggered my relfexion.

I also tried something "experimental": cancelling bottom friction (LAW OF BOTTOM FRICTION = 0) but with the source term applied on the first plane with ks = 0,01 m. The results were different than if I use LAW OF BOTTOM FRICTION = 5 with 0,01 m. I basically got almost nil velocities at the bottom and almost the average current on the plane no 2 (ie a much steeper profile than what I got with the regular approach). I was hoping to get roughly similar results which could have validated the approach for modelling surface roughness with a source term based on a similar quadratic friction law.

The surface slope is very small, less than 1.E-4.

Anyway, I will be away for 10 days now, so I can't test anything at the moment. But in case you have any suggestion I will test it when I am back.

Best regards
PL