Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source:...
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Transcript of Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source:...
![Page 1: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/1.jpg)
Linearized BC for the free surface in a gravity field
by Carlos Andrés Pérez Gutiérrez
Source: Axisa, sec. 1.3.2
![Page 2: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/2.jpg)
Fluid structrure coupling term at a wetted wall
• Viscous model, the fluid must adhere to the wall.
• Non viscous model, the fluid can slide freely
![Page 3: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/3.jpg)
![Page 4: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/4.jpg)
@ free surface
![Page 5: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/5.jpg)
• Gravity potential
• Virtual work of pressure
![Page 6: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/6.jpg)
• Lagrangian of the superficial fluid
• Principio de mínima acción
![Page 7: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/7.jpg)
• Principio de mínima acción:
•
Fuente: Wikipedia.
![Page 8: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/8.jpg)
• En la imagen aparecen una carga positiva fija (en rojo) y un electrón libre (en azul). De todas las trayectorias posibles, ¿cuál escogerá el electrón? El principio de acción mínima determina que la trayectoria 1 será la elegida.
![Page 9: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/9.jpg)
• Linearized aproximation of the boundary condition at the free surface
• Diffrentiating twice with respect to time, the surface condition in terms of pressure is obtained
![Page 10: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/10.jpg)
• The fluid particles must comply with two distinct conditions
Kinematical cosntrain
![Page 11: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/11.jpg)
Dynamical equilibrium
Bernoulli
![Page 12: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/12.jpg)
• Linealizando
• Deriving with respect to t and using the kinematical constrain
![Page 13: Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.](https://reader036.fdocuments.us/reader036/viewer/2022062808/5665b4cb1a28abb57c93bb8b/html5/thumbnails/13.jpg)