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TOPIC: Calculation of friction velocity UETCAR in TELEMAC3D

Calculation of friction velocity UETCAR in TELEMAC3D 5 years 3 months ago #34260

JBS
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Hello,

In TELEMAC3D, the friction velocity UETCAR is calculated in subroutine TFOND.f. The calculation seems to depend on the friction law used (2-3-4 on the one hand and 5 - Nikuradse - on the other hand).

For friction laws 2-3-4, UETCAR is obtained through the 2D velocity and the friction parameter. This is fine as it does not require to refine the vertical resolution near the bed, indeed, but it does not take advantage of the bottom velocity computed by assuming a logarithmic profile.

For friction law 5, UETCAR is obtained using the 3D bottom velocity, the bed layer thickness DIST and the bed roughness coefficient RUGOF as:

DO N=1,NPOIN
!  TAKES INTO ACCOUNT CRUSHED PLANES
!  I1 FIRST POINT WITH WATER ABOVE (EXCEPT CASE OF TIDAL FLATS
!  WHERE THE LEVEL UNDER THE FREE SURFACE IS TAKEN)
   I1=(MIN(NPLAN-1,IPBOT(N)+1)-1)*NPOIN+N
   DIST  = Z(NPOIN+I1)-Z(I1)
   AUX=MAX(1.001D0,30.D0*DIST/RUGOF(N))
   UETCAR(N)=(KARMAN/LOG(AUX))**2
           * (U3D(I1+NPOIN)**2+V3D(I1+NPOIN)**2)
ENDDO

In that case, I understand that the bottom velocity (in most general cases, I1=0) is assumed to be close to the mean value of the layer above it, but this is a little unclear...
Also, the assumption of a logarithmic profile implies that:

Umean_layer1 = (U*/kappa)*ln(30*Dz_layer1/e/ks)

Exp(1) should appear somewhere in the listing above, shouldn't it?

If I am mistaken please could you clarify:

- How is the bottom velocity defined in TELEMAC3D (according to the log profile it should be 0...) as well as the vertical discretization near the bed : is the plane defined at the bed exactly? or close? is any sub-layer assumed?...
- How is the expression for UETCAR derived when friction law = 5 then?

Thank you in advance for your help!
JBS.

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Calculation of friction velocity UETCAR in TELEMAC3D 5 years 3 months ago #34266

JBS
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Posts: 78
Thank you received: 3

I eventually found an answer to my questions so I put it here for whom it may be of interest.

Bottom velocities are computed exactly on the bed (plane 1), see #12083. When friction law = 5, friction velocity U* is calculated by considering plane 2, and as for a log profile:

U_plane2 = (U*/kappa)*ln[30*Dz/ks]

we get :

U* = U_plane2 * kappa / ln[30*Dz/ks]

This is what is coded in TFOND.f. Therefore, for a good estimate of U* the distance Dz between planes 1 and 2 should not be too large (i.e. a fine resolution near the bed is required).
Sometimes a factor of 33 appears instead of 30 inside the ln() but this is much likely to depend on the value taken for the van Karman constant (30 is for kappa = 0.40 I think).

For more considerations upon the physical meaning of the bottom velocity modelled in TELEMAC3D, post #12086 from JM Hervouet (2014) is quoted here below:

Plane 1 is indeed the bottom, but the velocity is not zero because it is supposed to be given at a small distance from the bottom,outside the viscous layer (think that it is subjected to turbulent viscosity), and also above the grain size. In fact the friction velocity is determined with the velocity of the second plane (see e.g. tfond.f), so this value of velocity on the bottom and the exact altitude over the bottom is not very important. My own theory is that it should be taken at delta(Z)/e**2, height of the first layer divided by the square of 2.71828.. In this case the discharge in the first layer computed with a linear interpolation of velocity gives the same discharge than with the integral of the logarithmic profile over the same layer... but this is a very mathematical point of view. We do not set this velocity to 0 because in the first layer and with linear interpolation it would give a wrong (too small) discharge.

JBS.

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