**TELEMAC MODELLING SYSTEM EXPLORATION**

Nicolas Cosqueric, 3rd year hydraulics student

**Presentation
of the task and definition of the objectives**
**Work done**
**Presentation
of the code ARTEMIS**
**Physical Background**
**Presentation
of a Maritime computation**

A first exploration of Telemac modelling system was made in the MCIP-A. The results of this first task was the exploration of Matisse, Telemac-2d and Rubens and the redaction of a manual concerning this 3 modules. So, in this first task, hydrodynamic computation was explored. Now, we want to see the two other main aspect of Telemac modelling system, that is to say transport and wave propagation. At least, we want to write a complete manual about the main utilisation of Telemac at ENSEEIHT.

The use of Artemis is quite complex at the beginning because it does not compute such as Telemac. Morover, since Telemac modelling system is only available on Windows machine, in the room C-112, There was problem of room reservation. Therefore, I explore only the code ARTEMIS and I wrote a manual wich describe the use of Telemac2d and Artemis.

The module ARTEMIS solves the BERKHOFF equations by a finite elements methods. Therefore, it takes into account wave reflexion, refraction and diffraction of a linear wave in a domain where the bottom height vary slowly. The applications fall into computation of wave propagation near coastal region such as computation of agitation in a port.At every point of the grid, ARTEMIS compute the velocity potential and deduce then the following results :

Wave heightWave directionPhasevelocity of the free flow

The current version of Artemis (version 3.0) computes also wave breaking and bottom friction.

A brief description of this effect is made for the students who does not know these effects :

Refraction : Refraction affects wave direction. It is linked to bottom topography or to current. (In artermis, linked to bottom topography). It is similar to the refraction phenomenon in optic.

Reflextion and diffraction : As for refraction, you have the same phenomenon in optics. This effect appears essentially in sea port.

Wave breaking : This effect appears in coastal region. There are several kinds of wave breaking

Physical Background

Wave propagation is completly described by the equations of Navier-Stockes. However, in order to solve this equations, some simplifications are made. In our case, wave propagation is represented by the equation of BERKHOFF which take into account reflexion, diffraction and refraction.Firstly, let us consider some notations :The equations of Berkhoff is deduced from the equations of Navier-Stockes with the following hypothesis :

no viscosityirrotationnal flow which allows to introduce the velocity potentialH/L <<1 : small curveH/h <<1low deep variationWith this simplifications, we obtain the equations of Berkhoff :

The form of the velocity potential is :

The equations which is solved :

Where C and Cg are respectively phase and group velocities

Simulation number 1

The bottom file represent a region near biarritz. The following picture represents this region :

As you can see on this picture, This the hight deep is about 20 meters. The lenght of the domain is about 3000 meters.

Definition of the grid

For a good computation with Artemis, we must have at least 7 points of computation per lenght. (It comes from a stability criteria).So, before a computation, we have to estimate the wave lenght in order to achieved a good computation. First, I decide to realize a test grid with a lenght mesh of 25 meters in order to learn this code (It leads to 7000 points in the grid). But if we want to estimate the wave lenght in this coastal region, we can show that this mesh lenght is to long. Indeed, if we consider the relation dispersion, wave lenght is given by the following formula :

In coastal region near Biarritz, we can think that wave period is about 7 meters. Therefore, the wave lenght is less than 70 meters (The wave lenght will decrease with the deep)

Therefore, a good choice is a mesh lenght of 10 meters in order to realize a good computation.

Definition of the boundary condition

The boundary condition type are defined in matisse as the following :

The boundary "large" is defined as a incident wave conditionThe boundary "plage" is defined as a solid frontierThe boundaries "bord1" and "bord2" as defined as free frontiers.Physical parameters

Wave directionPeriodWave heightfree surface height45°72

Results

Wave height :

As you can see on this picture, there is some wave height near the coastal region (in blue) which are higher than the height at the large. It is the effect of shoaling . The results along the boundary seems to be unrealistic. We can think that there is a problem on the boundary therefore we have to restrict the domain where we want to analyse results.

Wave phase

Wave phase permits to analyse the direction changes. In this case, it is quasi-uniform therefore there is not significant changes in the direction but this result is normal according to the wave direction at the boundary. Indeed, the waves propagate along a quasi-plane beach.

Simulation number 2

The bottom topography is modified. Indeed, we add a simple geometry with matisse which can represent and island.

Modification with Matisse

Artemis computation

The physical parameter are the same as in the simulation number 1.

Wave directionPeriodWave heightfree surface height45°720.3

Results of the computation

Wave phase :

Wave height