Water waves

Summary

Water waves are disturbances of the free surface of water that propagate under gravity, and for short waves also under surface tension. In the classical mathematical model the water is an ideal fluid in irrotational motion, and the unknown free surface is part of the problem. The model leads to a nonlinear free boundary problem for Laplace's equation. This problem is the starting point of the theories of linear waves, Stokes waves, solitary and cnoidal waves. Ocean swell, ship wakes and tsunamis are all water waves.