= Free surface
{title2=$z=\eta$}
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A <free surface> is a fluid interface whose position evolves as part of the solution. A water-air boundary provides a familiar example when the air's mechanical effect is approximated by a prescribed external <pressure>. Its motion obeys a <kinematic boundary condition>, while balance of <traction> supplies a dynamical condition involving <pressure>, viscous <stress> and, where relevant, <surface tension>.
For a surface $z=\eta(x,t)$ in two dimensions, the kinematic condition is $\eta_t+u\eta_x=w$ at the surface. A material particle already on the interface stays on it. The free-surface height is therefore coupled to the underlying <velocity field>, rather than being a fixed wall. Small disturbances generate <surface gravity waves> or capillary effects, depending on the relevant restoring force. Measuring both surface shape and flow tests different parts of this coupled problem.
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