 Kinematic boundary condition

A kinematic boundary condition requires a material boundary to move with the local material velocity in its normal direction. If the boundary is the level set $F(\mathbf{x},t)=0$, a particle staying on it satisfiesFor a two-dimensional fluid surface $z=\eta (x,t)$ this gives $w={\eta }_t+u{\eta }_x$, evaluated at the moving surface.

The term ${\eta }_t$ describes the surface height changing at a fixed position, while $u{\eta }_x$ accounts for a particle moving along a slope. At a stationary impermeable boundary, the condition reduces to zero relative normal flow. Tangential motion can still occur, so a separate no-slip boundary condition is needed when the wall model requires it. The kinematic condition specifies compatible motion; a stress or pressure balance supplies distinct dynamical information.