Analytical description of transient long waves like storm surges, surf beat and tsunami

The highly transient initial shapes of 1D forced long waves are described in analogy with the swinging up of a mass on a spring forced by a simple harmonic force. That is, the complete solution is seen as the asymptotic, steady forced wave plus free waves which cancel it in the initial state of rest. The highly transient, complete wave form subsequently grows as the free waves separate from the forced wave. This approach gives a clear understanding of many of the characteristics of storm surge, tsunami and surfbeat