Dynamic Boundary Condition.

Consider a wave propagating over a body of water, and assume ideal fluid and irrotational flow. Water for flow speeds much smaller than the sound speed in water can be considered as an incompressible fluid. Under the asumptions above, the velocity field $\vec{v}$ for the flow can be written as the gradient of a potential function $\phi(x,y,z)$.

At solid boundaries, like the bottom, the kinematic boundary condition prescribes the flow velocity normal to the body surface, which is

$$\vec{v}.\vec{n} = \nabla\phi.\vec{n} = 0 \mbox{ on the bottom surface,} \notag$$

since the bottom is at rest.

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