open TELEMAC-MASCARET The mathematically superior suite of solvers

The description of the wind parametrization in Telemac2d (section 6.3.1 of the Users' Manual) leaves something to desire. It is not really clear which formulas are implemented in the code and how the user can tuned them to his/her own purpose.

Normally the starting point is a presentation of the general parametrization based on dimensional analysis:


Dimensionally N/m² = kg/m³ * m²/s².

Since the shear is the same across the free surface, sometimes one can resort to the notion of friction velocity upon scaling the wind shear stress either with the air density (with a view to the atmospheric boundary layer) or with the water density (with a view to wind-driven currents within the body of water). For example, in cases ADCIRC requests that the wind shear is given to the solver as a squared friction velocity (m²/s²) based on the water density.

I guess this is acknowledged physics and terminology.

In the TELEMAC manual I read about a 'coefficient of wind influence' that is not clearly defined. One formula of the Institute of Oceanographic Sciences is mentioned. It concerns a quantity a_vent aka a_wind, which is a candidate drag coefficient, I presume.
IMHO, this formula lacks a specification of which parametrization it serves, not to mention that it is not crystal clear whether this a default used by TELEMAC, or one cautionary example meant to provide guidance (for which action?). There are some warnings about the manipulation of the unknown coefficient by the densities of air and water, but they suffer from the lack of a proper which is which.

Could this section be brought in line with the standard terminology used in the field?
Thanks in advance for considering this. Hope this helps

Apparently the request above has not made it to the action list. This is a second attempt to make a case for improvement.

Concerning the user manual [page 43-44, Version 7.2, 20 april 2017]

Document location:
${YOURPATH}/v7p2r1/documentation/telemac2d/user/telemac2d_user_v7p2.pdf#page=43

The user manual does define the coefficient of wind influence, alas in a chaotic way, but it does not explain it. The current structure of the reasoning is

1. the coefficient of wind influence hides complex phenomena --- the place of such coefficient of wind influence in the equations of motion has not been introduced;
2. the coefficient value can be obtained from many different formulas --- the coefficient of wind influence, one presumes, but wait;
3. a formula for the unnamed coefficient a_wind is given instead. Hence, neither the coefficient of wind influence nor such a coefficient a_wind have been defined yet;
4. an expression of the coefficient of the wind coefficient is eventually given,
   rho_air / rho_water * a_wind
   but the reader is left unguided about what a_wind is by name and physical meaning.

It would be nice if the order were 1 - 4 - 2 - 3 (and please read on)

.......................

The parent relationship of the coefficient of wind influence is explained in the book of Hervouet [1], page 14. This is the equilibrium of shear stress across the water-wind interface, expressed in kinematic units (L²/T²). Grossly paraphrased:

It would be nice if

• the quasi-universal name 'wind drag coefficient' and the quasi-universal symbol c_d are used for the mysterious coefficient a_wind;
• this formula is directly included in the user's manual, perhaps just simply as:
  shear stress on water = density air / density water * drag coefficient * squared wind velocity

so everybody understands at once.

.......................

Concerning the validation document [page 117, Version 7.2, 20 april 2017]

Document location: ${YOURPATH}/v7p2r1/documentation/telemac2d/validation/telemac2d_validation_v7p2.pdf#page=118

There:

1. neither by name nor by values does the validation document define a_wind. For such a limited additional information, the validation document refers to the book of Hervouet [1]. Since not everybody has the possibility to borrow or purchase this book, page 44 of the user manual could be a handier target;
2. The value of coefficient of wind influence applied to the test case is 1.2615 x 10^-3. However, since rho_wind / rho_water is of order 10^-3 and a_wind is of order 10^-3 too, I would rather expect that the coefficient of wind influence is of order 10^-6. This is also acknowledged in the user's manual:
   it is necessary to divide the value of a_wind by 1000 to obtain the value of the TELEMAC-2D keyword
   (1000 is yet approximate). By applying a coefficient of wind influence that is 1000 times larger, the wind speed is approximately 30 times larger than intended.

It would be nice if the test case '3.14 Wind set-up' is reviewed based on a correct order of magnitude of the (wind drag) coefficient.

I hope this illustrates how far one can get confused when dealing with Telemac and makes a good case for improvement (errors and omissions excepted, but not too many please).

.......................

[1] Hervouet, J-M. Hydrodynamics of free surface flows. Modelling with the finite element method. Wiley, 2007. ISBN 9780470035580

Hello

I will try to answer to some of your inquiries, I hope that you will arrive to a compromise.

I understand very well your criticism about
1- "quasi-universal name wind drag coefficient' and the quasi-universal symbol Cd are used for the mysterious coefficient a_wind".
2- "the reader is left unguided about what a_wind is by name and physical meaning."
3- the values of a_wind in the validation case is not clearly explained.

However,
1-you should keep in mind that people can have an other understanding (than yours) of the wind influence. Actually, unlike oceanic community which speaks about drag force, for most hydraulic community, wind effect is considered in a same way than friction effects on the bottom. This means that the wind forcing term is expressed as (along x axis) Fx=rho_air/rho_water*a_wind*Ux*SQRT(Ux²+Vy²)

which is not exactly the same expression of a drag force which can be written as F=0.5*rho*Cd*A*(Ux²+Vy²)
In a physical meaning, this latter is more like the effect of air on an airfoil which needs the definition of the famous drag coefficient but also the effective area.
Even though both physical understanding are a bit different, they reproduce exactly the same effect of the movement of a viscous fluid on a rough surface.
2- Thus, to switch from one meaning to an other, reader has to make a term-by-term identification which will bring him to your conclusion, i.e.:
awind/rhowater = 0.5*Cd, But this identification is only possible if you consider a semi-implicitation of the squared velocity (in order to have Fx=coeff*Ux*norm(U) and Fy=coeff*Uy*norm(U)).

I will add several sentences to explain the these ideas in the user manual in order to make things more clear. Tell me then if it will be more clear for you.
Finally for the validation case, I recognize that the explanation if cumbersome, I will add some comments to make it clearer.

I hope that this satisfies you.

with my best regards

Riadh ATA