The Effect of a Modulating Breakpoint on Bar-Trapped Waves

Abstract

Recent field observations of edge-waves on barred beaches show that bar-trapped modes can occur over the same frequency ranges as incident waves. Though 'co-incident' edge waves must derive their energy from the incident waves, they are unlikely to be forced directly by modulations in the radiation stress gradients caused by wave groups since these cause forcing at infragravity frequencies. However, the radiation stress patterns around the breakpoint are not quite sinusoidal in space and time, so that the forcing pattern in that region has components that occur at multiples of the group frequency and wavenumber. The forcing due to these higher order harmonics is contained within the zone between the maximum and minimum breakpoint. Since the degree to which energy is transferred to edgewaves depends on how similar the cross-shore shape of the forcing is relative to that of the exlgewave, transfer of energy to coincident edgewaves on barred beaches will be far more likely to occur over a wide range of frequencies than transfer to coincident edgewaves on plane beaches. Forcing conditions caused by incident wave group patterns are derived using a semi-numerical approach to demonstrate that co-incident edgewaves require a modulating breakpoint to occur. The degree to which the amount of forcing energy at higher order harmonics relative to that at the fundamental is shown to depend on the angle of incidence of the group at the breakpoint. INTRODUCTION Bar-trapped waves are Iongwaves trapped by refraction on longshore bars on beaches. They are unusual in that their amplitudes decay away from the bar rather than the shoreline as is the case for plane-beach solutions (Sch6nfeldt 1995, Bryan and Bowen 1996). Recent field evidence shows that these bar-trapped modes are energetic over a wide range of conditions, and over frequencies ranging from those measured in the traditional infragravity zone to well above the incident wave frequencies (Bryan et al. 1998, Bryan and Bowen 1998). 1) Research Scientist, National Institute of Water and Atmospheric Research, P.O. Box 1 l115, Hamilton, New Zealand. Email: k.bryan@~niwa.cri.nz