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 in two dimensions, the kinematic condition is 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.
In fluid mechanics and related fields, the term "free surface" refers to the boundary between a fluid (such as water or air) and another medium (such as air or a solid container) where the fluid is subjected to atmospheric pressure or pressure from the surrounding medium. This free surface is not constrained by any solid walls or surfaces and can move or deform freely.
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