Dispersion (water Waves) - Surface Tension Effects

Surface Tension Effects

Further information: Capillary wave

In case of gravity–capillary waves, where surface tension affects the waves, the dispersion relation becomes:

 \omega^2 = \left( g k + \frac{\sigma}{\rho} k^3 \right) \tanh (kh),

with σ the surface tension (in N/m).

For a water–air interface (with σ = 0.074 N/m and ρ = 1000 kg/m³) the waves can be approximated as pure capillary waves – dominated by surface-tension effects – for wavelengths less than 0.4 cm (0.2 in). For wavelengths above 7 cm (3 in) the waves are to good approximation pure surface gravity waves with very little surface-tension effects.

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