linearized bc for the free surface in a gravity field by carlos andrés pérez gutiérrez source:...
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Linearized BC for the free surface in a gravity field
by Carlos Andrés Pérez Gutiérrez
Source: Axisa, sec. 1.3.2
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
@ 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