What is the kinematic conditions for free-surface

[Chuck88]

When I am studying the Rayleigh-Taylor instability, I saw this equation:

$$\frac{\partial \eta}{\partial t} + u' \frac{\partial \eta}{\partial x} = \omega ' (\eta)$$

I do not quite understand the meaning of this equation. Can some one provide me with some instructions and information.

The detailed information of Rayleigh-Taylor instability is presented below.

http://en.wikipedia.org/wiki/Rayleigh-Taylor_instability

 

[OldEngr63]

Without trying to wade through the meaning of your equation (I don't know what your symbols mean, etc), the basic kinematic condition for a free surface is that the velocity vector must be tangent to the surface, or stated differently, the component of velocity normal to the free surface must be zero.

 

[AlephZero]

the basic kinematic condition for a free surface is that the velocity vector must be tangent to the surface, or stated differently, the component of velocity normal to the free surface must be zero.

That is only true is the free surface is not moving. The general condition is that the normal components of the fluid velocity and the free surface velocity are equal.

 

[OldEngr63]

AlephZero is correct.