Abstract
On the basis of the theory for infragravity waves induced by short-wave groups developed by Schäffer (1993), three-dimensional infragravity waves are analysed. The theory relies on the linearized depth-integrated conservation equations for mass and momentum combined to give a second-order long-wave equation with forcing expressions in terms of the radiation stress. This forcing gives a dynamic set-up originating from oscillations of the break-point position and a dynamic set-down bound to the short-wave groups. For small angles of incidence leaky-mode solutions are found while trapped modes appear when the primary waves are sufficiently oblique. In the latter case resonant edge-wave excitation may occur. A semi-analytical steady-state solution for the infragravity motion is presented. The solution is restricted to periodicity along a plane beach connected to a shelf and valid only for small primary-wave modulations.
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