Linear Evolution of a Narrow-Banded Surface Gravity Wavepacket Over an Infinite Step

This paper focuses on the classical and fundamental problem of waves propagating over an infinite step in finite water depth. Specifically, this paper aims to extend classical narrow-banded wave theory for constant water depth which uses a multiple-scales expansion to the case of an abrupt change in the water depth, known as an infinite step. This paper derives the linear evolution equations and is the first step towards the calculation of second-order and higher-order effects for wavepackets travelling over a step using commonly employed envelope-type evolution equations, in particular the bound sub- and super-harmonics at second order.