A free surface is a fluid boundary whose position is part of the solution and whose traction is prescribed by the adjoining medium. Its motion obeys a kinematic boundary condition, while its pressure or stress supplies a dynamic boundary condition.
A surface gravity wave is a free-surface oscillation restored by gravity. In inviscid deep water its angular frequency and horizontal wavenumber satisfy .
For two inviscid layers of equal depth between rigid lids, with lower density and upper density , a horizontal mode of wavenumber satisfiesThe sign reverses when the heavier fluid is above, producing the Rayleigh-Taylor instability.
A small-amplitude deep-water wave with surface elevation has dispersion relation and a velocity potential that decays as below the surface.
For small kinematic viscosity , the mean viscous dissipation per unit horizontal area is . Since the mean wave energy is , the amplitude obeys
For small-amplitude potential flow beneath a mean surface , the linearized kinematic and dynamic conditions are
In a rectangular box with Neumann side walls, a horizontal modehas horizontal wavenumber , depth dependence in infinitely deep fluid, and natural frequency .
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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.