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I am studying long-term morphodynamic evolution (order years to hundred of years) of an idealized estuary that is connected to the open sea (see attached figure) using Telemac2D+Sisyphe. At the southern boundary of the open sea i prescribe an M2 vertical tidal wave (option 544), which travels from south to north (see figure). At the northern boundary i use boundary option 444 (everything free) in combination with Thompson. At the western boundary, i prescribe 222. At the boundaries of the estuary i use also 222. In the attached figure, i also indicated the type of boundary conditions i use in Telemac2D. For Sisyphe i impose that LIEBOR=5 and EBOR=0 at the southern/western/northern boundaries to ensure that no bed level change takes place at these boundaries. For sediment formulation i use total load formula of Enguland & Handson (option=30). For other parameters in the cas files of Telemac2D/Sisyphe i use their default values.
Depth in the open sea is constant (=-30 m);

If i run a simulation (Telemac2D+Sisyphe), the bed level at the northern and southern boundaries does change, meaning that erosion is not 0 over there. I find this strange because it contradicts the fact that i impose that EBOR=0 at these locations. Furthermore, by studying the residual current at the southern and northern boundaries i found out that a residual current appears a these boundaries, which gives rise to sediment transport and thus bed level change. Apparently, the model does not properly deal with propagating tidal wave at these boundaries, even when using thompson. Ideally, i want no residual currents at these boundaries. As i study long-term morphodynamic evolution, the small erosion/deposition patterns appearing at the southern/northern boundaries keep on growing in time.

I tried many different configurations to be able to solve this problem, but i keep getting erosion-deposition patterns appearing at these boundaries. One of the things i tried, e.g., is to run a test case where i run only Telemac2D for a larger domain of the open sea. Next, i compute water levels+velocities at the southern and northern boundaries. Finally, i use these water level+velocities to force the model, using option 566. I tried also 466.
Unfortunately, this did not solve the problem.

I would be very grateful if somebody would help me on this problem. Are there other possibilities to impose other boundary conditions, like neumann boundary conditions or Riemann invariants (as the case in Delft3D for example). All suggestions or workarounds how to solve this problem are very welcome.
Please let me know if something is not clear.

Looking forward to hear you.

Kind regards,

Abdel

Attachment: model domain+type of boundary conditions

Unfortunately, nobody responded so far. Maybe i am asking too much. The thing is that i really would like to do long-term morphology with Telemac, and according to many studies with Delft3D (Roelvink & Walstra 2004; Ridderinkhof et al., 2004...) it has been demonstrated that imposing water levels at the offshore boundaries and gradients of waterlevels at the lateral boundaries (see attached figure) are the most suitable boundary conditions to do long-term morphology in estuaries and tidal inlets.
The only thing i would like to know how to program gradients of water level elevation at the boundaries (Neumann). I was reading in the book of Mr. JM Hervouet (Hydrodynamics of sea surface flows with finite element method) that Neumann boundary conditions are used in the k-epsilon model.
I am realizing that programming a gradient of water level is maybe a hell of job in Telemac and that maybe i am asking too much in this forum. Any suggestions of how to impose water level gradients would be very welcome.




Thank you very much.
Looking forward to hearing from you soon

Abdel Nnafie
Flanders Hydraulics Research
Antwerp, Belgium

Sorry about lack of reply.

You are specifying an offshore frictionless wall (222) so that except for the estuary you have a wave along a channel. Presumably this is considered to be a progressive wave so you are alllowing it to escape to the north.

I think this should work as long as Coriolis is neglected with the north boundary as a wave absorbing one. Usually we specify the water level and velocity and then let the Thompson condition sort it out. It may also be possible to use the TELEMAC2D incident wave boundary condition. The standard test case for an absorbing boundary is the Gouttedo validation case.

Did you mean to specify zero normal water level gradient at the offshore boundary? You could code a normal (u) velocity at that wall based on the gradient of the water level normal to the boundary (in BORD). It might help to have structured mesh along the wall. Then you should be able to minimise the normal level gradient. Or even you could try to enforce a non-zero normal gradient.

Good Luck

Alan Cooper

Dear Mr. Cooper,

Thank you very much for your suggestions. I will try them and report my results as soon as i got them.

Have a nice weekend


Kind regards,

Abdel Nnafie
Flanders Hydraulics Research
Antwerp, Belgium

Hello,

I do not know exactly what is the problem in your case, and I am not even sure that it is well posed, as the prescribed tidal wave does not take into account the discharge of the river, that should normally influence this boundary also. Moreover when the flow enters the Northern boundary it may be difficult to find the correct entering velocities, all is in the hands of Thompson boundary conditions. As a matter of fact Thompson conditions probably work better in deep waters with small velocities. They are based also in Riemann invariants. It is a tentative method to correct problems that are not well posed, but do not expect miracles and put these conditions as far as possible of shallow waters. In your case alternating boundary conditions 5 4 4 and 4 5 5 depending on the tidal flux entering or exiting a boundary is also something to look at, without any Thompson.

Another thing on Thompson: if you take subroutine thomps.f in your Fortran file, you will find a hardcoded relaxation coefficient TETA=1.D0. You may try lower values and see if it cancels or delays the residual current.

On the gradient of water level I am ready to learn a new thing but really do not understand how to introduce it in the equations. In finite elements our boundary conditions naturally appear in the formulation, like fluxes through liquid boundaries, or stresses on solid boundaries, they stem from physical terms, and this way of dealing with so-called "essential" boundary conditions gives a proof of conservation of mass, momentum, etc. Even imposing a depth is not so natural and must be handled with care, it spoils the mass conservation of water, so we would need a sound theory on how to prescribe water level gradients for implementing it.

With best regards,

Jean-Michel Hervouet

Dear Mr. Hervouet,

Thank you very much for your suggestions and for clarifying that imposing gradients of water levels are difficult to impose within finite elements approach. I will report my findings as soon as possible.

Have a nice weekend


Kind regards,

Abdel Nnafie
Flanders Hydraulics Research
Antwerp, Belgium