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ANSWER - flume experiment - wave propagation in estuary : Différence entre versions

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= Context=
 
= Context=
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<big>[[ANSWER_-_Essais_en_canal_-_propagation_de_vagues_en_estuaire_schématique#Position_des_sections_de_mesure|French Version]]</big>
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This page is part of the collaborative initiative ANSWER relative to the elaboration and dissemination of scientific knowledge in water resources
 
This page is part of the collaborative initiative ANSWER relative to the elaboration and dissemination of scientific knowledge in water resources
  
It concerns
+
It concerns the following topics:
 
* MARITIME HYDRAULICS
 
* MARITIME HYDRAULICS
 
* WAVE PROPAGATION IN ESTUARY
 
* WAVE PROPAGATION IN ESTUARY
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The physical model tests were conducted from April to August 2016 at SIWRR by Hazeme Mohamed as part of her 2nd year internship at ENTPE, proposed by Jean-Michel Tanguy (SHF) and supervised by Professor San Dinh Director of SIWRR.
 
The physical model tests were conducted from April to August 2016 at SIWRR by Hazeme Mohamed as part of her 2nd year internship at ENTPE, proposed by Jean-Michel Tanguy (SHF) and supervised by Professor San Dinh Director of SIWRR.
  
The SIWRR is home to several experimental facilities that study the behavior of waves near the coast.
+
The SIWRR is home to several experimental facilities for studying the behavior of waves near the coast.
  
 
We used the 40 m long, 1.2 m wide and 1.5 m maximum depth canal. It includes a wave maker that can generate regular and irregular waves, with a maximum amplitude of 0.42m, period between 0.5s and 5s. At its upstream end, the beach may be absorbent or reflective.
 
We used the 40 m long, 1.2 m wide and 1.5 m maximum depth canal. It includes a wave maker that can generate regular and irregular waves, with a maximum amplitude of 0.42m, period between 0.5s and 5s. At its upstream end, the beach may be absorbent or reflective.
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In order to build a database necessary for the validation of the theoretical developments, 3 types of tests were carried out:
 
In order to build a database necessary for the validation of the theoretical developments, 3 types of tests were carried out:
  
# '''SmAbUn''' : runs in a rectangular uniform smooth bottom flume with absorbing upstream beach  
+
# '''SmAbUn''' : runs in a rectangular uniform smooth bottom flume with an absorbing upstream beach  
# '''RoAbUn''' : runs in a rectangular uniform partially rocky covered bottom flume with absorbing upstream beach  
+
# '''RoAbUn''' : runs in a rectangular uniform partially rocky covered bottom flume with an absorbing upstream beach  
# '''SmAbCo''' : runs in a rectangular convergent banks and absorbing upstream beach  
+
# '''SmAbCo''' : runs in a rectangular flume with convergent banks and absorbing upstream beach  
  
 
By varying the parameters below, it is more than 68 different tests that have been instrumented:
 
By varying the parameters below, it is more than 68 different tests that have been instrumented:
 
* Regular waves
 
* Regular waves
 
* Constant slope along 10 m upstream of the channel: 1/25.
 
* Constant slope along 10 m upstream of the channel: 1/25.
* Different templates: rectangular canal and canal with linearly bank reduction.
+
* Different geometries: rectangular canal or canal with linearly bank reduction.
 
* Variation of the bottom roughness of the channel (smooth bottom with sand and bottom covered with rocks)
 
* Variation of the bottom roughness of the channel (smooth bottom with sand and bottom covered with rocks)
 
* Varying conditions at the upstream boundaries: absorption or reflection.
 
* Varying conditions at the upstream boundaries: absorption or reflection.
 
* Variation of different wave parameters: water level, amplitude and period
 
* Variation of different wave parameters: water level, amplitude and period
  
Afin de faciliter le repérage des essais, nous avons établis la nomenclature suivante:
+
In order to simplify the identification of the runs, we have established the following nomenclature:
* Profondeur amont au niveau du batteur à houle : D65 ou D70 correspondant à des profondeurs de 65cm et de 70cm
+
* Upstream depth at the wave maker: D65 or D70 corresponding to depths of 65cm and 70cm
* A4 : amplitude de l'onde : 4cm (demi-amplitude : l'amplitude réelle est de 8 cm comptée de tête à creux)
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* Amplitude of the wave: A4 = 4cm (half-amplitude: the real amplitude is 8 cm counted from head to trough)
* T4 : période de l'onde : 4s
+
* Wave period: T4 = 4s
* Etat des fonds : Sm (Smooth) ou Ro (Rocks)
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* Bottom surface: Sm (Smooth) or Ro (Rocks)
* Conditions limites amont : Re (réflexion) ou Ab (Absorption)
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* Upstream boundary conditions: Re (reflection) or Ab (Absorption)
* Configuration de la section : Un (canal rectangulaire de section constante) ou Co (canal rectangulaire de section convergente linéaire)
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* Geometry of the section: Un (rectangular channel of constant section) or Co (rectangular channel with linear convergent section)
Par exemple, le fichier D70A2T7_RoAbCo correspond à une houle régulière générée en amont avec une hauteur d'eau de 70cm, une amplitude de 2cm, une période de 7s sur un fond constitué dans sa partie pentue de roches avec une plage absorbantes dans un canal convergent.
+
For example, the file D70A2T7_RoAbCo corresponds to a regular canal. Waves are generated upstream with a water height of 70cm, an amplitude of 2cm, a period of 7s on a bottom constituted in its sloping part of rocks with an absorbing beach in a convergent canal.
Les suffixes _D et _E sont ajoutés aux noms de fichiers pour signifier qu'il s'agit de données et d'exploitation des données.
+
The _D and _E suffixes are added to the file names corresponding to Data and Exploitation.
  
Les combinaisons de paramètres sont les suivantes (toutes les combinaisons n'ont pas été testées):
+
The combinations of parameters are as follows (not all combinations have been tested):
 
{| class="wikitable"
 
{| class="wikitable"
 
|-
 
|-
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|}
 
|}
  
Les quelques photos et videos suivantes illustrent la configuration des lieux:
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The following photos and videos illustrate the configurations:
  
 
{|
 
{|
 
|-
 
|-
| [[File:DSCN4335.JPG|300px|thumb|Vue générale du canal vers le batteur à houle]] ||  [[File:page4image1829824.jpg|300px|thumb|Vue générale du canal vers l'amont]] || [[File:page4image3802432.jpg|300px|thumb|Vue latérale du canal]] ||  
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| [[File:DSCN4335.JPG|300px|thumb|General view towards the wave maker ]] ||  [[File:page4image1829824.jpg|300px|thumb|General view upstream]] || [[File:page4image3802432.jpg|300px|thumb|Lateral viewl]] ||  
 
|-
 
|-
|  [[File:DSCN4339.JPG|300px|thumb|Vue de la plage d'absorption amont ]]  || [[File:page6image1829600.jpg|300px|thumb|Lit de cailloux (partiel)]] ||  
+
|  [[File:DSCN4339.JPG|300px|thumb|Upstream beach ]]  || [[File:page6image1829600.jpg|300px|thumb|Rocks on the bed (partial)]] ||  
 
|-
 
|-
| [[File:IMGP0158.JPG|300px|thumb|Berges convergentes]] || [[File:page7image3807808.png|300px|thumb|Berges convergentes]]
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| [[File:IMGP0158.JPG|300px|thumb|Convergents banks]] || [[File:page7image3807808.png|300px|thumb|Convergent banks]]
 
|}
 
|}
  
Voici également quelques vidéos tournées au SIWRR sur le vrai canal dans des conditions voisines de nos essais, mais avec une condition limite qui ne correspond pas à nos scénarios.
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Here are also some videos records at SIWRR of the channel in conditions close to our tests, but with boundary conditions not corresponding to our scenarios.
  
 
<html><iframe frameborder="0" width="480" height="270" src="//www.dailymotion.com/embed/video/x6div6m" allowfullscreen allow="autoplay"></iframe></html>
 
<html><iframe frameborder="0" width="480" height="270" src="//www.dailymotion.com/embed/video/x6div6m" allowfullscreen allow="autoplay"></iframe></html>
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<html><iframe frameborder="0" width="480" height="270" src="//www.dailymotion.com/embed/video/x6div6p" allowfullscreen allow="autoplay"></iframe></html>
 
<html><iframe frameborder="0" width="480" height="270" src="//www.dailymotion.com/embed/video/x6div6p" allowfullscreen allow="autoplay"></iframe></html>
  
== Position des sections de mesure ==
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== Locations of the measuring sections ==
Le canal comprend 2 parties : une première partie de 10 m de long caractérisée par une pente de 1/25 qui se poursuit par une partie à pente nulle jusqu'à la condition limite représentée soit par une plage absorbante (schéma ci-dessous) soit par un mur réfléchissant.
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The channel consists of two parts: a first part of 10 m long characterized by a slope of 1/25 which continues with an horizontal part until the boundary condition represented either by an absorbing beach (diagram below) or by a reflective wall.
  
[[File:Canal position sections.jpeg|600px]]
 
  
Les sections de mesures ont été positionnées tous les 2,5 m en partant du début de la pente jusqu'à la section x=10m. Les sections 6 et 7 sont respectivement à X=12m et X=14 m
+
{|
 +
|-
 +
| [[File:Canal position sections.jpeg|600px|thumb|Plane vue uniform canal]] || [[File:profil convergent.jpeg|500px|thumb|Longitudinal profile convergent canal  ]]
 +
|}
  
= Exploitation des essais =
+
The measurement sections were positioned every 2.5 m from the beginning of the slope to the section x = 10m. Sections 6 and 7 are respectively at X = 12m and X = 14m
Nous présentons ci-dessous 4 essais qui nous semblent représentatifs des typologies de configurations, puis nous comparons ensuite plusieurs essais similaires en faisant varier 1 seul paramètre à la fois (la période, l'amplitude, la rugosité, l'effet de convergence...)
+
 
== Présentation de 4 essais types ==
+
= Exploitation of measurements =
 +
We present below 4 runs which seem to us representative of the typologies of the configurations. Then we compare several similar runs by varying one parameter at a time (the period, the amplitude, the roughness, the convergence effect).
 +
== Presentation of 4 standard tests ==
 
=== SmAbUn ===
 
=== SmAbUn ===
Nous choisissons l'essai D70A4T4_SmAbUn qui correspond aux paramètres suivants:
+
We choose test D70A4T4_SmAbUn which corresponds to the following parameters:
  
'''Profondeur : 70cm, Amplitude 4cm, Période 4s, Fond lisse, Absorption amont, Gabarit constant'''
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'' 'Depth: 70cm, half Amplitude 4cm, Period 4s, Smooth bottom, Absorption upstream, Uniform cross sections' ''
  
Le graphique ci-dessus représente les enregistrements temporels des 7 capteurs placés le long du canal. Ils sont indiqués avec des couleurs différentes. Nous avons sélectionné une fenêtre temporelle qui correspond à une série de vagues bien formées comprises entre les limites suivantes : les premières vagues sont inexploitables à cause de le mise en mouvement du batteur et les suivantes sont perturbées correspondant à des phénomènes parasites : apparition d'ondes transversales et retour des ondes depuis la plage qui n'est pas totalement absorbante.
+
Figure 1 represents the time records of the 7 measurement devices along the channel. They are indicated with different colors. We have selected a time window that corresponds to a series of well-formed waves between the following limits: the first waves are unusable because of the movement of the wave maker and the last ones are disturbed corresponding to parasitic phenomena: transverse wave appearance and/or wave return from the not fully absorbent beach.
 +
 
 +
Thus, thanks to this diagram, we can illustrate several parameters whose longitudinal variations can be highlighted on the following graphs, but also the appearance of local disturbances.
  
Ainsi, grâce à ce schéma, nous pouvons illustrer plusieurs paramètres dont les variations longitudinales peuvent-être mises en évidence sur les graphiques suivants, mais également l'apparition des perturbations locales au droit des capteurs.
 
 
[[File:Graphique_D70A4T4  - SmAbUn .png|left|800px|thumb|Figure 1]]
 
[[File:Graphique_D70A4T4  - SmAbUn .png|left|800px|thumb|Figure 1]]
  
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|}
 
|}
  
Interprétations des schémas
+
Diagrams interpretations
* Figure 2 : Conformément à la théorie, l'amplitude des ondes augmente longitudinalement le long de la pente du fond
+
* Figure 2: In accordance with the theory, the wave amplitude increases upstream along the bottom slope
* Figure 3 : Variation des pentes amont et aval des ondes de propagation. Le graphique montre très bien le raidissement de la pente amont de l'onde (en rouge) et la diminution de la pente aval : ceci illustre l'importance de processus non-linéaires. Nous verrons qu'ils diminuent avec l'amplitude et la période de l'onde. En valeurs absolues, la pente du raidissement amont est supérieure à celle de l'affaissement aval.
+
* Figure 3: Variation of the upstream and downstream slopes of the propagation waves (see Annex to see how the two slopes are calculated). The graph shows very well the stiffening of the upstream slope of the wave (in red) and the decrease of the downstream slope: this illustrates the importance of non-linear processes. We will see that they decrease with the amplitude and the period of the wave. In absolute values, the slope of the upstream stiffening is greater than that of the downstream decreasing.
* Figure 4 : la célérité des ondes diminue et reste très proche des valeurs théoriques données par la théorie des grandes ondes. On note cependant un point particulier situé à la limite amont de la pente (X=10m)
+
* Figure 4: the celerity of the waves decreases and remains very close to the theoretical values ​​given by the theory of long waves. There is however a particular point located at the upstream limit of the slope (X = 10m)
* Figure 5 : La longueur d'onde diminue le long de la pente. Le point de rupture de pente est également apparent  
+
* Figure 5: The wavelength decreases along the slope. The break point of slope is also apparent.
  
Remarque :  
+
Note :
Au droit de la section X=10 m, la célérité est voisine de 1,5 m/s Ainsi pour un trajet aller-retour de 2x20m = 40 m pour revenir au profil X=14m, l'onde va mettre un temps voisin de 27 s. Ainsi le graphique de la figure 1 se situe avant que l'onde réfléchie (éventuelle) en provenance de la plage absorbante ne revienne perturber les capteurs.
+
At section X = 10m, the speed is close to 1.5 m/s. Thus for a return trip of 2x20m = 40 m to return to the profile X = 14m, the wave takes 27 s. Thus the graph of Figure 1 is before the reflected wave (if any) from the absorbing range does disturb the sensors.
  
 
=== RoAbUn ===
 
=== RoAbUn ===
Nous choisissons l'essai D70A4T4_RoAbUn qui correspond aux paramètres suivants:
 
  
'''Profondeur : 70cm, 1/2 Amplitude 4cm, Période 4s, Fond roches, Absorption amont, Gabarit constant'''
+
We choose run D70A4T4_RoAbUn which corresponds to the following parameters:
 +
 
 +
'' 'Depth: 70cm, 1/2 Amplitude 4cm, Period 4s, Rocky bottom, Absorption upstream, Uniform canal' ''
  
De manière similaire avec les autres essais décrits ci-dessus, nous pouvons illustrer plusieurs paramètres dont les variations longitudinales peuvent-être mises en évidence sur les graphiques suivants.
+
In a similar way to the other tests described above, we can illustrate several parameters whose longitudinal variations can be highlighted on the following graphs.
 
[[File:Graphique_D70A4T4  - RoAbUn .png|left|800px|thumb|Figure 6]]
 
[[File:Graphique_D70A4T4  - RoAbUn .png|left|800px|thumb|Figure 6]]
  
 
{|
 
{|
|-
+
| -
| [[File:Amplitude_D70A4T4 - RoAbUn .png|400px|thumb|Figure 7]] || [[File:Steepness_D70A4T4 - RoAbUnV2 .png|400px|thumb|Figure 8]]
+
| [[File: Amplitude_D70A4T4 - RoAbUn .png | 400px | thumb | Figure 7]] || [[File: Steepness_D70A4T4 - RoAbUnV2 .png | 400px | thumb | Figure 8]]
|-
+
| -
| [[File:Celerity_D70A4T4  - RoAbUn .png|400px|thumb|Figure 9]] || [[File:Lenght_D70A4T4 - RoAbUn .png|400px|thumb|Figure 10]]
+
| [[File:Celerity_D70A4T4  - RoAbUn .png|400px|thumb|Figure 9]] || [[File: Lenght_D70A4T4 - RoAbUn .png | 400px | thumb | Figure 10]]
 
|}
 
|}
  
Interprétations des schémas:
+
Interpretations:
* Figure 7 : Conformément à la théorie, l'amplitude des ondes augmente longitudinalement le long la pente du fond
+
* Figure 7: According to the theory, the wave amplitude increases longitudinally along the bottom slope
* Figure 8 : Variation des pentes amont et aval des ondes de propagation. Le graphique montre très bien le raidissement de la pente amont de l'onde (en rouge) et la diminution de la pente aval : ceci illustre l'importance de processus non-linéaires. Nous verrons qu'ils diminuent avec l'amplitude et la période de l'onde. En valeurs absolues, la pente du raidissement amont est supérieure à celle de l'affaissement aval.
+
* Figure 8: Variation of the upstream and downstream slopes of the propagation waves. The graph shows very well the stiffening of the upstream slope of the wave (in red) and the decrease of the downstream slope: this illustrates the importance of non-linear processes. We will see that they decrease with the amplitude and the period of the wave. In absolute values, the slope of the upstream stiffening is greater than that of the downstream decreasing.
* Figure 9 : la célérité des ondes diminue et reste très proche des valeurs théoriques données par la théorie des grandes ondes. On note le même le même point singulier situé à la limite amont de la pente que dans l'essai précédent (X=10m)
+
* Figure 9: the celerity of the waves decreases and remains very close to the theoretical values ​​given by the theory of the long waves. The same singular point is found at the upstream limit of the slope as in the previous test (X = 10m)
* Figure 10 : La longueur d'onde diminue le long de la pente. Le point de rupture de pente est également apparent.
+
* Figure 10: The wavelength decreases along the slope. The upstream point of slope change is also apparent.
  
Remarque : Au droit de la section X=12 m, la célérité est voisine de 1,5 m/s. Ainsi pour un trajet aller-retour de 2x20m = 40 m pour revenir au profil X=14m, l'onde va mettre un temps voisin de 27 s. Ainsi le graphique de la figure 6 se situe avant que l'onde réfléchie (éventuelle) en provenance de la plage absorbante ne revienne perturber les capteurs.
+
Note: At the right of section X = 12 m, the speed is close to 1.5 m / s. Thus for a round trip of 2x20m = 40 m to return to the profile X = 14m, the wave will put a time close to 27 s. Thus the graph of FIG. 6 is located before the reflected wave (if any) from the absorbing pad returns to disturb the sensors.
  
 
=== SmAbCo ===
 
=== SmAbCo ===
  
Nous choisissons ici l'essai D70A4T4_SmAbCo qui correspond aux valeurs des paramètres suivants:  
+
We choose run D70A4T4_SmAbCo which corresponds to the following parameters :  
  
'''Profondeur : 70cm, 1/2 Amplitude 4cm, Période4 s, Fond lisse, Absorption amont, Berges convergentes'''
+
'' 'Depth: 70cm, 1/2 Amplitude 4cm, Period 4s, Smooth Bottom, Absorption upstream, Convergent banks' ''
  
De manière similaire avec les autres essais décrits ci-dessus, nous pouvons illustrer plusieurs paramètres dont les variations longitudinales peuvent-être mises en évidence sur les graphiques suivants:  
+
In a similar way to the other tests described above, we can illustrate several parameters whose longitudinal variations can be illustrate on the following graphs:
  
 
[[File:Graphique_D70A4T4_SmAbCo.png|800px|left|thumb|Figure 11]]
 
[[File:Graphique_D70A4T4_SmAbCo.png|800px|left|thumb|Figure 11]]
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|}
 
|}
  
Interprétations des schémas:
+
Interpretations:
* Figure 12 : Conformément à la théorie, l'amplitude des ondes augmente longitudinalement le long la pente du fond
+
* Figure 12: According to the theory, the wave amplitude increases longitudinally along the slope of the bottom
* Figure 13 : Variation des pentes amont et aval des ondes de propagation. Le graphique montre très bien le raidissement de la pente amont de l'onde (en rouge) et la diminution de la pente aval : ceci illustre l'importance de processus non-linéaires. Nous verrons qu'ils diminuent avec l'amplitude et la période de l'onde. En valeurs absolues, la pente du raidissement amont est supérieure à celle de l'affaissement aval.
+
* Figure 13: Variation of the upstream and downstream slopes of the propagation waves. The graph shows very well the stiffening of the upstream slope of the wave (in red) and the decrease of the downstream slope: this illustrates the importance of non-linear processes. We will see that they decrease with the amplitude and the period of the wave. In absolute values, the slope of the upstream stiffening is greater than that of the downstream decreasing.
* Figure 14 : la célérité des ondes diminue et reste très proche des valeurs théoriques données par la théorie des grandes ondes. On note le même le même point singulier situé à la limite amont de la pente que dans l'essai précédent (X=10m)
+
* Figure 14: the celerity of the waves decreases and remains very close to the theoretical values ​​given by the theory of the long waves. The same singular point is found at the upstream limit of the slope as in the previous test (X = 10m)
* Figure 15 : La longueur d'onde diminue le long de la pente. Le point de rupture de pente est également apparent.
+
* Figure 15: The wavelength decreases along the slope. The upstream point of slope change is also apparent.
  
Remarque : Au droit de la section X=12 m, la célérité est voisine de 1,5 m/s Ainsi pour un trajet aller-retour de 2x20m = 40 m pour revenir au profil X=14m, l'onde va mettre un temps voisin de 27 s. Ainsi le graphique de la figure 11 se situe avant que l'onde réfléchie (éventuelle) en provenance de la plage absorbante ne revienne perturber les capteurs.
+
Note: At section X = 12 m, the speed is close to 1.5 m / s Thus for a return trip of 2x20m = 40 m to return to the profile X = 14m, the wave takes 27 s. Thus, the graph of Figure. 11 is located before the (eventual) reflected wave coming from the absorbing upstream boundary, which can disturb the sensors.
  
== Analyse comparative des enregistrements ==
+
== Comparative analysis of records ==
Nous avons exploité l'ensemble des essais de manière transversale, de manière à mettre en oeuvre des comportements particuliers des ondes de surface.
+
We have exploited some of the tests in a transversal manner, to identify particular behaviors of the surface waves:
C'est ainsi que nous mènerons des comparaisons sur les paramètres suivants:
+
* impact of the variation of the amplitude for several tests characterized by the same parameters but with roughnesses, or geometries either uniform, or linear
* impact de la variation de l'amplitude pour plusieurs essais caractérisés par les mêmes paramètres mais avec des rugosités, et un gabarit soit uniforme, soit linéaire
+
* impact of the change in the period
* impact de la variation de la période
+
* impact of the variation of the initial amplitude
* impact de la variation de l'amplitude initiale
+
* comparison for the same test carried out in uniform or converging section
* comparaison pour un même essai réalisé en section uniforme ou convergente
+
* impact of roughness variation
* impact de la variation de la rugosité
+
=== Impact of the variation of the amplitude for several tests with the same parameters ===
=== Impact de la variation de l'amplitude pour plusieurs essais avec les mêmes paramètres ===
+
We have compared several tests characterized by D70, by Ab absorbing boundary conditions and for the same period T5.
Nous avons comparé plusieurs essais caractérisé par D70, par des conditions limites absorbantes Ab et pour une même période T5.  
+
These are tests D70A5T5, D70A2T2 and D70A5T7 in RoAbUn, SmAbCo and SmAbUn conditions
Il s'agit des essais D70A5T5, D70A2T2 et D70A5T7 en conditions RoAbUn, SmAbCo et SmAbUn
+
 
{|
 
{|
 
|-
 
|-
Ligne 179 : Ligne 186 :
 
|}
 
|}
  
* Figure 16 : les variations d'amplitudes pour les 3 schémas sont croissantes suivant la pente, ce qui est bien conforme à la théorie.  
+
* Figure 16: amplitudes variations for the 3 runs are increasing according to the slope, which is in accordance with the theory.
* Figure 17 : les amplitudes initiales des vagues générées par le batteur ne sont pas toujours bien respectées : toutes les courbes d'un même schéma devraient partir du même point à X=0
+
* Figure 17: the initial amplitudes of the waves generated by the wave maker are not always well respected: all the curves of the same diagram should start from the same point to X = 0
* Figure 18 : on note une chute très nette de l'amplitude à l'arrivée en haut de la pente.
+
* Figure 18: there is a sharp change in amplitude at the arrival at the top of the slope.
  
=== Impact de la variation de la période sur les conditions de propagation des ondes ===
+
=== Impact of period variation on wave propagation conditions ===
Nous avons choisi la configuration du canal rectangulaire D70A4 avec berges convergentes (SmAbCo) et avons comparé des essais réalisés avec des périodes différentes (T2, T4,T5 et T6)
+
We chose the configuration of rectangular channel D70A4 with convergent banks (SmAbCo) and compare tests realized with different periods (T2, T4, T5 and T6)
 
{|
 
{|
 
|-
 
|-
Ligne 191 : Ligne 198 :
 
| [[File:Celerity_D70A4 - Wave amplitude variation .png|400px|thumb|Figure 21]] || [[File:G2_D70A4_Length.png|400px|thumb|Figure 22]]
 
| [[File:Celerity_D70A4 - Wave amplitude variation .png|400px|thumb|Figure 21]] || [[File:G2_D70A4_Length.png|400px|thumb|Figure 22]]
 
|}
 
|}
Commentaires:
 
* Figure 19 : l'amplitude augmente le long de la pente, sauf pour la période la plus basse (T2) qui décroit en haut de pente. Les courbes T4 et T5 sont assez voisines. La courbe T6 est plus basse car elle ne part pas de la même origine
 
* Figure 20 : les pentes des vagues de faibles fréquences sont très proches en valeur absolue et évoluent peu, ce qui montre le caractère quasi-linéaire de la propagation. Pour les fréquences plus importantes, le raidissement amont et plus important en valeur absolue que l'affaissement aval. Cet affaissement se maintient à une valeur proche de 1% alors que le raidissement augmente progressivement en montant la pente
 
* Figure 21 : toutes les vagues de même amplitude se propagent vers l'amont avec une célérité décroissante voisine de -0,1 m/s/ml, ce qui peut s'écrire : <math> dC/dX=-0,1</math>. Après la rupture de pente, la célérité tend à prendre une valeur constante voisine de 1,6 m/s
 
* Figure 22 : la longueur d'onde décroit vers l'amont avec une intensité variant avec l'amplitude.
 
  
Des schémas précédents, nous pouvons en déduire les relations empiriques suivantes : sachant que L=CT, la loi de variation de la longueur d'onde dL/dX=dC/dx*T=-0.1*T, qui peut être vérifiée sur la figure 22
+
Comments
 +
* Figure 19: the amplitude increases along the slope, except for the lowest period (T2) which decreases at the top of the slope. The curves T4 and T5 are quite similar. The curve T6 is lower because it does not start from the same origin
 +
* Figure 20: The slopes of low frequency waves are very close in absolute value and evolve little, which shows the quasi-linear nature of the propagation. For larger frequencies, upstream stiffening are larger in absolute value than downstream decreasing, which is maintained at a value close to 1% while the stiffening increases gradually along the slope
 +
* Figure 21: all waves of the same amplitude propagate upstream with a decreasing speed close to -0.1 m / s / ml, which can be written as: <math>dC / dX = -0.1</math> . After the point-break of slope, the celerity tends to take a constant value close to 1.6 m / s
 +
* Figure 22: the wavelength decreases upstream with intensity varying with amplitude.
  
=== Impact de la variation de l'amplitude sur les conditions de propagation des ondes ===
+
From previous figures, we can deduce the following empirical relationships: knowing that '''''L = CT''''', the law of variation of the wavelength '''''dL / dX = dC / dx * T = -0.1 * T''''', which can be checked on the figure 22
Afin de mettre en évidence l'impact de la variation de l'amplitude sur les conditions de propagation des ondes, nous avons choisi de comparer plusieurs essais qui correspondent à D70T4 mais avec des amplitudes différentes : A2, A4 et A5 dans les configuration SmAbCo (fond lisse, condition limite amont absorbante et berges convergentes)
+
 
 +
=== Impact of amplitude variation on wave propagation ===
 +
In order to highlight the impact of the amplitude variation on the wave propagation conditions, we chose to compare several tests corresponding to D70T4 but with different amplitudes: A2, A4 and A5 in the SmAbCo configuration ( smooth bottom, absorbent upstream boundary and convergent banks)
 
{|
 
{|
 
|-
 
|-
Ligne 208 : Ligne 216 :
 
|}
 
|}
  
Commentaires:
+
Comments
* Figure 23 : l'amplitude augmente le long de l'axe proportionellement à la valeur de l'amplitude initiale. Pour la plus faible amplitude initiale, la vague ne "gonfle pas": l'amplitude reste constante le long de la pente, ce qui confirme le caractère quasi-linéaire de l'essai
+
* Figure 23: The amplitude increases along the axis proportionally to the value of the initial amplitude. For the lowest initial amplitude, the wave does not "increase": the amplitude remains constant along the slope, which confirms the quasi-linear nature of the test
* Figure 24 : les pentes des courbes amont de raidissement sont plus importantes que les courbes aval d'affaissement
+
* Figure 24: the slopes of the upstream curves of stiffening are more important than the downstream curves of subsidence
* Figure 25 : la vitesse de  d'onde a tendance à diminuer de manière uniforme quelle que soit l'amplitude initiale
+
* Figure 25: The wave speed tends to decrease uniformly regardless of the initial amplitude
* Figure 26 : la longueur d'onde a tendance à diminuer de manière uniforme quelle que soit l'amplitude initiale avec une pente voisine de 30%
+
* Figure 26: the wavelength tends to decrease uniformly regardless of the initial amplitude with a slope close to 30%
Des schémas précédents, on peut déduire les 2 relations empiriques suivantes:
+
From previous schemes, we can deduce the following 2 empirical relationships:
 
'''''L=-0,3*X+10,5 et C=-1/12*X+2,6'''''
 
'''''L=-0,3*X+10,5 et C=-1/12*X+2,6'''''
  
=== Mise en évidence de l'effet de convergence des berges par rapport au canal uniforme===
+
=== Demonstration of the convergence effect of the banks with respect to the uniform canal ===
Nous avons choisi de comparer 2 essais D70A4T4 : SmAbUn et SmAbCo
+
We chose to compare 2 runs D70A4T4: SmAbUn and SmAbCo
 
{|
 
{|
 
|-
 
|-
Ligne 227 : Ligne 235 :
 
|}
 
|}
  
Commentaires:
+
Comments
* les différences entre les courbes Un et Co apparaissent à partir du sommet de la pente (X=10m)
+
* the differences between the curves Un and Co appear on each graph from the top of the slope (X = 10m)
* pour les basses périodes (Figures 26, 27, 28 et 31) on observe une chute brutale de l'amplitude en deçà de l'amplitude de départ au niveau du batteur (X=0m)
+
* for low periods (Figures 26, 27, 28 and 31) there is a sharp drop in amplitude below the starting amplitude at the wave maker (X = 0m)
* plus la fréquence augmente (Figures 28, 29, 30), moins la courbe Co décroche vers le bas
+
* the smaller the period is (Figures 28, 29, 30), the lower the curve Co decreases
  
=== Impact de la rugosité des fonds sur les conditions de propagation des ondes ===
+
=== Impact of bottom roughness on wave propagation conditions ===
Nous avons choisi 2 essais D70A4T4 et comparé l'effet des configurations SmAbUn et RoAbUn
+
We chose 2 D70A4T4 runs and compare the SmAbUn and RoAbUn configurations
 
{|
 
{|
 
|-
 
|-
Ligne 241 : Ligne 249 :
 
|}
 
|}
  
Commentaires:
+
Comments
* Figure 32 : la modification des amplitudes n'est pas très importante en intensité. Cependant, une rugosité plus importante provoque un amortissement de l'amplitude des ondes
+
* Figure 32: the change of amplitudes is not very important in intensity. However, a greater roughness causes a damping of the wave amplitude
* Figure 33 : on note peu de modifications concernant le raidissement dont et l'affaissement aval des ondes
+
* Figure 33: There are few modifications concerning the stiffening and the decreasing of the waves
* Figure 34 : peu de différences pour la célérité qui diminue tout au long de la pente, avec cependant la présence dans les 2 cas d'un pic de vitesse au point haut de la rupture de pente
+
* Figure 34: few differences in celerity decreasing along the slope, with however the presence in both cases of a peak celerity at the high point of the slope failure
* Figure 35 : peu de différences pour la longueur d'onde qui diminue tout au long de la pente, avec cependant la présence dans les 2 cas d'un pic de longue d'onde au point haut de la rupture de pente
+
* Figure 35: few differences for the wavelength that decreases along the slope, with however the presence in both cases of a long wave peak at the high point of the slope failure
  
=== Apparition d'un point particulier en X=10m ===
+
=== Appearance of a particular point in X = 10m ===
Dans les courbes ci-dessus, apparait une discontinuité au point amont de rupture de pente. Plusieurs hypothèses peuvent être avancées: ou bien le capteur n'a pas bien fonctionné, ou il a été implanté au mauvais endroit ou encore il se passe un phénomène particulier en ce point.
+
In the curves above, there is a discontinuity at the upstream point of slope failure. Several hypotheses can be advanced: either the sensor did not work well, or it was implanted in the wrong place or there is a particular phenomenon at this point.
  
Remarquons que tous les essais réalisés en canal uniforme (SmAbUn et RoSmUn) présentent ce point alors que les essais réalisés en canal convergent (SmAbCo) ne le montrent pas.
+
Note that all the runs carried out in uniform channel (SmAbUn and RoSmUn) present this point whereas the tests carried out in convergent channel (SmAbCo) do not show it.
  
==Annexe==
+
== Annex ==
  
 
{|
 
{|
Ligne 262 : Ligne 270 :
 
|}
 
|}
  
=Conclusion=
+
= Conclusion =
== Résultats des essais ==
+
== Test results ==
Les essais réalisés au SIWRR sont intéressants à plusieurs titres:
+
The tests conducted at SIWRR are interesting in several ways:
* ils permettent de mettre en évidence le comportement des ondes longues lorsqu'elles progressent dans un estuaire de forme rectangulaire, dont le fond est caractérisé par une pente régulière ascendante vers l'amont (exemple : estuaire de la Gironde). Deux configurations de variation de sections ont été étudiées : uniforme sur l'ensemble du canal d'une part et convergentes vers l'amont d'autre part.
+
* They make possible to highlight the behavior of long waves as they progress in an estuary of rectangular shape, whose bottom is characterized by a regular slope ascending upstream (example: estuary of the Gironde). Two geometries of variation of sections were studied: uniform on the whole channel on the one hand and convergent upstream on the other hand.
* ils ont permis de construire une base de données en libre disposition sur internet
+
* they made it possible to build a database freely available on the internet
* Comparativement aux théories, ils ont permis de vérifier les points suivants:
+
* Compared to theories, they allowed to verify the following points:
:* l'amplitude des ondes augmente vers l'amont à cause de la pente du fond ascendante augmentée par la restriction de gabarit dans la configuration aux berges convergentes
+
: * the wave amplitude increases upstream because of the slope of the rising bottom and also increased by the restriction of sections with convergent banks in these cases
:* la cambrure des vagues reste assez homogène dans le cas de faibles amplitudes et de faibles périodes, ce qui montre que la progression est quasi-linéaire. Mais plus les amplitudes augmentent ou que la période est grande, les vagues se raidissent sur leur face amont et s'affaissent sur leur face aval.
+
: * the curve of the waves remains fairly homogeneous in the case of small amplitudes and weak periods, which shows that the progression is quasi-linear. But the greater the amplitudes or the period is large, the waves stiffen on their upstream face and collapse on their downstream face.
:* les longueurs d'ondes diminuent vers l'amont
+
: * wavelengths decrease upstream
:* le comportement particulier de la déformations des ondes au point de rupture de pente amont (X=10 m) n'est pas explicable.
+
: * the particular behavior of the wave deformations at the point of upstream slope failure (X = 10 m) is not explicable.
== Recommandations aux modélisateurs ==
+
== Recommendations to modellers ==
Compte tenu des choix des paramètres dans l'ensemble de ces essais, il est recommandé aux modélisateurs de tester plusieurs types de modèles:
+
Given the choice of parameters in all of these tests, modelers are recommended to test several types of models:
* les configurations les plus intéressantes au sens de la richesse des données produites sont D70AiTj (i=2,4,5 et j=2,4,5,6)
+
* the most interesting configurations in the sense of the richness of the data produced are D70AiTj (i = 2,4,5 and j = 2,4,5,6)
* il est probable que la forte pente du fond rende les modèles de Saint-Venant difficiles à utiliser, mais il convient de les tester
+
* it is likely that the steep slope makes the Saint-Venant models difficult to use, but it is worthwhile to test them
* des modèles linéarisés peuvent être utilisés pour les faibles amplitudes et les basses périodes
+
* linearized models can be used for low amplitudes and low periods
* les non-linéarités doivent être caractérisées en débranchant chaque terme non linéaire : vitesse ou frottement, pour mettre en évidence leurs impacts respectifs
+
* non-linearities must be characterized by disconnecting each non-linear term: celerity or friction, to highlight their respective impacts
* Il est recommandé de reproduire les courbes de sensibilité à l'amplitude et à la période (essais D70AiTj)
+
* It is recommended to reproduce amplitude and period sensitivity curves (tests D70AiTj)
* Il convient également d'analyser finement ce qui se passe au point de rupture de pente amont (entre le pente et l'horizontale à l'abscisse X=10m). Les essais ont mis en évidence des particularités de la propagation des ondes et un examen précis des résultats en ce point doit être mené
+
* It is also necessary to finely analyze what happens at the point of upstream slope failure (between the slope and the horizontal at the abscissa X = 10m). Some tests have shown particularities of wave propagation at this point, that must be examined
* la comparaison des résultats de modélisations des modèles numériques avec la solution analytique linéaire dans les cas de canal uniforme et de canal aux berges convergentes est tout à fait pertinente dans la mesure où on se situe dans des configurations quasi-linéaires (faible période / faible amplitude)
+
* the comparison of numerical modeling model results with the linear analytical solution in the case of uniform canal and convergent banks canal is quite relevant in quasi linear configurations (weak period, weak amplitude)
 +
 
 +
= Authors and acknowledgments =
 +
* Hazeme Mohamed: tests conducted at SIWRR in Saigon, Vietnam
 +
* Jean-Michel Tanguy: exploitation of the essays and writing of this page
  
= Auteurs=
+
We thank Prof. San Dinh, director of the Southern Institute of Water Resources Research in Saigon, Vietnam, for allowing the completion of these trials, the mentoring of the trainee. These tests were made possible thanks to the financing of ENTPE as part of the FORM @ HYDRO project. We would like to thank in particular Bernard Clément, Director of the City & Environment Department, HDR Teacher-Researcher at LEHNA-IPE, ENTPE
* Hazeme Mohamed : réalisation des essais au SIWRR de Saigon au Vietnam  
+
* Jean-Michel Tanguy : exploitation des essais et rédaction de cette page
+
  
Nous remercions le professeur San Dinh directeur du Southern Institute of Water Resources Research à Saigon au Vietnam pour avoir permis la réalisation de ces essais, l'encadrement de la stagiaire. Ces essais ont pu être réalisés grâce au financement de l'ENTPE dans le cadre de l'opération FORM@HYDRO. Nous tenons à remercier plus particulièrement Bernard Clément, Directeur du Département Ville & Environnement, Enseignant-chercheur HDR au LEHNA-IPE, Ecole Nationale des Travaux Publics de l'Etat
+
[[Catégorie:ANSWER]]
 +
[[Catégorie:Simulation_sur_modèle_physique]]

Version actuelle en date du 7 mars 2018 à 21:56

Sommaire

[modifier] Context

French Version

This page is part of the collaborative initiative ANSWER relative to the elaboration and dissemination of scientific knowledge in water resources

It concerns the following topics:

  • MARITIME HYDRAULICS
  • WAVE PROPAGATION IN ESTUARY

It is closely related to 2 others pages:

To validate these theoretical approaches, a series of flume experiments were conducted at Southern Institute of Water Resources Research (SIWRR) in Saigon - Vietnam.

[modifier] Experimental set-ups

[modifier] Nomenclature of tests

The physical model tests were conducted from April to August 2016 at SIWRR by Hazeme Mohamed as part of her 2nd year internship at ENTPE, proposed by Jean-Michel Tanguy (SHF) and supervised by Professor San Dinh Director of SIWRR.

The SIWRR is home to several experimental facilities for studying the behavior of waves near the coast.

We used the 40 m long, 1.2 m wide and 1.5 m maximum depth canal. It includes a wave maker that can generate regular and irregular waves, with a maximum amplitude of 0.42m, period between 0.5s and 5s. At its upstream end, the beach may be absorbent or reflective.

In order to build a database necessary for the validation of the theoretical developments, 3 types of tests were carried out:

  1. SmAbUn : runs in a rectangular uniform smooth bottom flume with an absorbing upstream beach
  2. RoAbUn : runs in a rectangular uniform partially rocky covered bottom flume with an absorbing upstream beach
  3. SmAbCo : runs in a rectangular flume with convergent banks and absorbing upstream beach

By varying the parameters below, it is more than 68 different tests that have been instrumented:

  • Regular waves
  • Constant slope along 10 m upstream of the channel: 1/25.
  • Different geometries: rectangular canal or canal with linearly bank reduction.
  • Variation of the bottom roughness of the channel (smooth bottom with sand and bottom covered with rocks)
  • Varying conditions at the upstream boundaries: absorption or reflection.
  • Variation of different wave parameters: water level, amplitude and period

In order to simplify the identification of the runs, we have established the following nomenclature:

  • Upstream depth at the wave maker: D65 or D70 corresponding to depths of 65cm and 70cm
  • Amplitude of the wave: A4 = 4cm (half-amplitude: the real amplitude is 8 cm counted from head to trough)
  • Wave period: T4 = 4s
  • Bottom surface: Sm (Smooth) or Ro (Rocks)
  • Upstream boundary conditions: Re (reflection) or Ab (Absorption)
  • Geometry of the section: Un (rectangular channel of constant section) or Co (rectangular channel with linear convergent section)

For example, the file D70A2T7_RoAbCo corresponds to a regular canal. Waves are generated upstream with a water height of 70cm, an amplitude of 2cm, a period of 7s on a bottom constituted in its sloping part of rocks with an absorbing beach in a convergent canal. The _D and _E suffixes are added to the file names corresponding to Data and Exploitation.

The combinations of parameters are as follows (not all combinations have been tested):

D (cm) A (cm) T (s)
65 2 2
70 4 4
5 5
6
7

The following photos and videos illustrate the configurations:

General view towards the wave maker
General view upstream
Lateral viewl
Upstream beach
Rocks on the bed (partial)
Convergents banks
Convergent banks

Here are also some videos records at SIWRR of the channel in conditions close to our tests, but with boundary conditions not corresponding to our scenarios.

[modifier] Locations of the measuring sections

The channel consists of two parts: a first part of 10 m long characterized by a slope of 1/25 which continues with an horizontal part until the boundary condition represented either by an absorbing beach (diagram below) or by a reflective wall.


Plane vue uniform canal
Longitudinal profile convergent canal

The measurement sections were positioned every 2.5 m from the beginning of the slope to the section x = 10m. Sections 6 and 7 are respectively at X = 12m and X = 14m

[modifier] Exploitation of measurements

We present below 4 runs which seem to us representative of the typologies of the configurations. Then we compare several similar runs by varying one parameter at a time (the period, the amplitude, the roughness, the convergence effect).

[modifier] Presentation of 4 standard tests

[modifier] SmAbUn

We choose test D70A4T4_SmAbUn which corresponds to the following parameters:

'Depth: 70cm, half Amplitude 4cm, Period 4s, Smooth bottom, Absorption upstream, Uniform cross sections'

Figure 1 represents the time records of the 7 measurement devices along the channel. They are indicated with different colors. We have selected a time window that corresponds to a series of well-formed waves between the following limits: the first waves are unusable because of the movement of the wave maker and the last ones are disturbed corresponding to parasitic phenomena: transverse wave appearance and/or wave return from the not fully absorbent beach.

Thus, thanks to this diagram, we can illustrate several parameters whose longitudinal variations can be highlighted on the following graphs, but also the appearance of local disturbances.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5

Diagrams interpretations

  • Figure 2: In accordance with the theory, the wave amplitude increases upstream along the bottom slope
  • Figure 3: Variation of the upstream and downstream slopes of the propagation waves (see Annex to see how the two slopes are calculated). The graph shows very well the stiffening of the upstream slope of the wave (in red) and the decrease of the downstream slope: this illustrates the importance of non-linear processes. We will see that they decrease with the amplitude and the period of the wave. In absolute values, the slope of the upstream stiffening is greater than that of the downstream decreasing.
  • Figure 4: the celerity of the waves decreases and remains very close to the theoretical values ​​given by the theory of long waves. There is however a particular point located at the upstream limit of the slope (X = 10m)
  • Figure 5: The wavelength decreases along the slope. The break point of slope is also apparent.

Note : At section X = 10m, the speed is close to 1.5 m/s. Thus for a return trip of 2x20m = 40 m to return to the profile X = 14m, the wave takes 27 s. Thus the graph of Figure 1 is before the reflected wave (if any) from the absorbing range does disturb the sensors.

[modifier] RoAbUn

We choose run D70A4T4_RoAbUn which corresponds to the following parameters:

'Depth: 70cm, 1/2 Amplitude 4cm, Period 4s, Rocky bottom, Absorption upstream, Uniform canal'

In a similar way to the other tests described above, we can illustrate several parameters whose longitudinal variations can be highlighted on the following graphs.

Figure 6
-
Figure 7
Figure 8
-
Figure 9
Figure 10

Interpretations:

  • Figure 7: According to the theory, the wave amplitude increases longitudinally along the bottom slope
  • Figure 8: Variation of the upstream and downstream slopes of the propagation waves. The graph shows very well the stiffening of the upstream slope of the wave (in red) and the decrease of the downstream slope: this illustrates the importance of non-linear processes. We will see that they decrease with the amplitude and the period of the wave. In absolute values, the slope of the upstream stiffening is greater than that of the downstream decreasing.
  • Figure 9: the celerity of the waves decreases and remains very close to the theoretical values ​​given by the theory of the long waves. The same singular point is found at the upstream limit of the slope as in the previous test (X = 10m)
  • Figure 10: The wavelength decreases along the slope. The upstream point of slope change is also apparent.

Note: At the right of section X = 12 m, the speed is close to 1.5 m / s. Thus for a round trip of 2x20m = 40 m to return to the profile X = 14m, the wave will put a time close to 27 s. Thus the graph of FIG. 6 is located before the reflected wave (if any) from the absorbing pad returns to disturb the sensors.

[modifier] SmAbCo

We choose run D70A4T4_SmAbCo which corresponds to the following parameters :

'Depth: 70cm, 1/2 Amplitude 4cm, Period 4s, Smooth Bottom, Absorption upstream, Convergent banks'

In a similar way to the other tests described above, we can illustrate several parameters whose longitudinal variations can be illustrate on the following graphs:

Figure 11
Figure 12
Figure 13
Figure 14
Figure 15

Interpretations:

  • Figure 12: According to the theory, the wave amplitude increases longitudinally along the slope of the bottom
  • Figure 13: Variation of the upstream and downstream slopes of the propagation waves. The graph shows very well the stiffening of the upstream slope of the wave (in red) and the decrease of the downstream slope: this illustrates the importance of non-linear processes. We will see that they decrease with the amplitude and the period of the wave. In absolute values, the slope of the upstream stiffening is greater than that of the downstream decreasing.
  • Figure 14: the celerity of the waves decreases and remains very close to the theoretical values ​​given by the theory of the long waves. The same singular point is found at the upstream limit of the slope as in the previous test (X = 10m)
  • Figure 15: The wavelength decreases along the slope. The upstream point of slope change is also apparent.

Note: At section X = 12 m, the speed is close to 1.5 m / s Thus for a return trip of 2x20m = 40 m to return to the profile X = 14m, the wave takes 27 s. Thus, the graph of Figure. 11 is located before the (eventual) reflected wave coming from the absorbing upstream boundary, which can disturb the sensors.

[modifier] Comparative analysis of records

We have exploited some of the tests in a transversal manner, to identify particular behaviors of the surface waves:

  • impact of the variation of the amplitude for several tests characterized by the same parameters but with roughnesses, or geometries either uniform, or linear
  • impact of the change in the period
  • impact of the variation of the initial amplitude
  • comparison for the same test carried out in uniform or converging section
  • impact of roughness variation

[modifier] Impact of the variation of the amplitude for several tests with the same parameters

We have compared several tests characterized by D70, by Ab absorbing boundary conditions and for the same period T5. These are tests D70A5T5, D70A2T2 and D70A5T7 in RoAbUn, SmAbCo and SmAbUn conditions

Figure 16
Figure 17
Figure 18
  • Figure 16: amplitudes variations for the 3 runs are increasing according to the slope, which is in accordance with the theory.
  • Figure 17: the initial amplitudes of the waves generated by the wave maker are not always well respected: all the curves of the same diagram should start from the same point to X = 0
  • Figure 18: there is a sharp change in amplitude at the arrival at the top of the slope.

[modifier] Impact of period variation on wave propagation conditions

We chose the configuration of rectangular channel D70A4 with convergent banks (SmAbCo) and compare tests realized with different periods (T2, T4, T5 and T6)

Figure 19
Figure 20
Figure 21
Figure 22

Comments

  • Figure 19: the amplitude increases along the slope, except for the lowest period (T2) which decreases at the top of the slope. The curves T4 and T5 are quite similar. The curve T6 is lower because it does not start from the same origin
  • Figure 20: The slopes of low frequency waves are very close in absolute value and evolve little, which shows the quasi-linear nature of the propagation. For larger frequencies, upstream stiffening are larger in absolute value than downstream decreasing, which is maintained at a value close to 1% while the stiffening increases gradually along the slope
  • Figure 21: all waves of the same amplitude propagate upstream with a decreasing speed close to -0.1 m / s / ml, which can be written as: $ dC / dX = -0.1 $ . After the point-break of slope, the celerity tends to take a constant value close to 1.6 m / s
  • Figure 22: the wavelength decreases upstream with intensity varying with amplitude.

From previous figures, we can deduce the following empirical relationships: knowing that L = CT, the law of variation of the wavelength dL / dX = dC / dx * T = -0.1 * T, which can be checked on the figure 22

[modifier] Impact of amplitude variation on wave propagation

In order to highlight the impact of the amplitude variation on the wave propagation conditions, we chose to compare several tests corresponding to D70T4 but with different amplitudes: A2, A4 and A5 in the SmAbCo configuration ( smooth bottom, absorbent upstream boundary and convergent banks)

Figure 23
Figure 24
Figure 25
Figure 26

Comments

  • Figure 23: The amplitude increases along the axis proportionally to the value of the initial amplitude. For the lowest initial amplitude, the wave does not "increase": the amplitude remains constant along the slope, which confirms the quasi-linear nature of the test
  • Figure 24: the slopes of the upstream curves of stiffening are more important than the downstream curves of subsidence
  • Figure 25: The wave speed tends to decrease uniformly regardless of the initial amplitude
  • Figure 26: the wavelength tends to decrease uniformly regardless of the initial amplitude with a slope close to 30%

From previous schemes, we can deduce the following 2 empirical relationships: L=-0,3*X+10,5 et C=-1/12*X+2,6

[modifier] Demonstration of the convergence effect of the banks with respect to the uniform canal

We chose to compare 2 runs D70A4T4: SmAbUn and SmAbCo

Figure 26
Figure 27
Figure 28
Figure 29
Figure 30
Figure 31

Comments

  • the differences between the curves Un and Co appear on each graph from the top of the slope (X = 10m)
  • for low periods (Figures 26, 27, 28 and 31) there is a sharp drop in amplitude below the starting amplitude at the wave maker (X = 0m)
  • the smaller the period is (Figures 28, 29, 30), the lower the curve Co decreases

[modifier] Impact of bottom roughness on wave propagation conditions

We chose 2 D70A4T4 runs and compare the SmAbUn and RoAbUn configurations

Figure 32
Figure 33
Figure 34
Figure 35

Comments

  • Figure 32: the change of amplitudes is not very important in intensity. However, a greater roughness causes a damping of the wave amplitude
  • Figure 33: There are few modifications concerning the stiffening and the decreasing of the waves
  • Figure 34: few differences in celerity decreasing along the slope, with however the presence in both cases of a peak celerity at the high point of the slope failure
  • Figure 35: few differences for the wavelength that decreases along the slope, with however the presence in both cases of a long wave peak at the high point of the slope failure

[modifier] Appearance of a particular point in X = 10m

In the curves above, there is a discontinuity at the upstream point of slope failure. Several hypotheses can be advanced: either the sensor did not work well, or it was implanted in the wrong place or there is a particular phenomenon at this point.

Note that all the runs carried out in uniform channel (SmAbUn and RoSmUn) present this point whereas the tests carried out in convergent channel (SmAbCo) do not show it.

[modifier] Annex

Graphique calcul pentes.jpg
  • Upsream slope : US = A*Dt3/(L*Dt1)
  • Downstream slope : DS = A*Dt3/(L*Dt2)
  • L = Distance between 2 gauges

[modifier] Conclusion

[modifier] Test results

The tests conducted at SIWRR are interesting in several ways:

  • They make possible to highlight the behavior of long waves as they progress in an estuary of rectangular shape, whose bottom is characterized by a regular slope ascending upstream (example: estuary of the Gironde). Two geometries of variation of sections were studied: uniform on the whole channel on the one hand and convergent upstream on the other hand.
  • they made it possible to build a database freely available on the internet
  • Compared to theories, they allowed to verify the following points:
* the wave amplitude increases upstream because of the slope of the rising bottom and also increased by the restriction of sections with convergent banks in these cases
* the curve of the waves remains fairly homogeneous in the case of small amplitudes and weak periods, which shows that the progression is quasi-linear. But the greater the amplitudes or the period is large, the waves stiffen on their upstream face and collapse on their downstream face.
* wavelengths decrease upstream
* the particular behavior of the wave deformations at the point of upstream slope failure (X = 10 m) is not explicable.

[modifier] Recommendations to modellers

Given the choice of parameters in all of these tests, modelers are recommended to test several types of models:

  • the most interesting configurations in the sense of the richness of the data produced are D70AiTj (i = 2,4,5 and j = 2,4,5,6)
  • it is likely that the steep slope makes the Saint-Venant models difficult to use, but it is worthwhile to test them
  • linearized models can be used for low amplitudes and low periods
  • non-linearities must be characterized by disconnecting each non-linear term: celerity or friction, to highlight their respective impacts
  • It is recommended to reproduce amplitude and period sensitivity curves (tests D70AiTj)
  • It is also necessary to finely analyze what happens at the point of upstream slope failure (between the slope and the horizontal at the abscissa X = 10m). Some tests have shown particularities of wave propagation at this point, that must be examined
  • the comparison of numerical modeling model results with the linear analytical solution in the case of uniform canal and convergent banks canal is quite relevant in quasi linear configurations (weak period, weak amplitude)

[modifier] Authors and acknowledgments

  • Hazeme Mohamed: tests conducted at SIWRR in Saigon, Vietnam
  • Jean-Michel Tanguy: exploitation of the essays and writing of this page

We thank Prof. San Dinh, director of the Southern Institute of Water Resources Research in Saigon, Vietnam, for allowing the completion of these trials, the mentoring of the trainee. These tests were made possible thanks to the financing of ENTPE as part of the FORM @ HYDRO project. We would like to thank in particular Bernard Clément, Director of the City & Environment Department, HDR Teacher-Researcher at LEHNA-IPE, ENTPE

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