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

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Transcripción de la presentación:

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

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

@ free surface

Gravity potential Virtual work of pressure

Lagrangian of the superficial fluid Principio de mínima acción

Principio de mínima acción: Fuente: Wikipedia.

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.

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

The fluid particles must comply with two distinct conditions Kinematical cosntrain

Dynamical equilibrium Bernoulli

Linealizando Deriving with respect to t and using the kinematical constrain