Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2.

Presentación del tema: "Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2."— Transcripción de la presentación:

1 Linearized BC for the free surface in a gravity field by Carlos Andrés Pérez Gutiérrez Source: Axisa, sec. 1.3.2

2 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

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4 @ free surface

5 Gravity potential Virtual work of pressure

6 Lagrangian of the superficial fluid Principio de mínima acción

7 Principio de mínima acción: Fuente: Wikipedia.

8 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.

9 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

10 The fluid particles must comply with two distinct conditions Kinematical cosntrain

11 Dynamical equilibrium Bernoulli

12 Linealizando Deriving with respect to t and using the kinematical constrain

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