Kinematic boundary condition for a free-surface graph
= Kinematic boundary condition for a free-surface graph
For a free surface $z=\eta(x,y,t)$ and velocity $(u,v,w)$, material conservation of $z-\eta$ gives
$$
w=\eta_t+u\eta_x+v\eta_y=\frac{D\eta}{Dt}
$$
on the surface.