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Subsections

1.3.1 Kinematic Boundary conditions

1.3.1.1 vertical

at fixed and moving $ r$ surfaces we set (see figure 1.15):

$\displaystyle \dot{r}=0$    at $\displaystyle r=R_{fixed}(x,y)$ (ocean bottom, top of the atmosphere) (1.7)

$\displaystyle \dot{r}=\frac{Dr}{Dt}$    at $\displaystyle r=R_{moving}$ (ocean surface,bottom of the atmosphere) (1.8)

Here

$\displaystyle R_{moving}=R_{o}+\eta$    

where $ R_{o}(x,y)$ is the `$ r-$ value' (height or pressure, depending on whether we are in the atmosphere or ocean) of the `moving surface' in the resting fluid and $ \eta $ is the departure from $ R_{o}(x,y)$ in the presence of motion.

1.3.1.2 horizontal

$\displaystyle \vec{\mathbf{v}}\cdot \vec{\mathbf{n}}=0$ (1.9)

where $ \vec{\mathbf{n}}$ is the normal to a solid boundary.

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