Energy transfer between short wave groups and bound long waves on a plane slope

Abstract

The present report describes a laboratory study on energy transfer between short wave groups and bound long waves. From previous experiments (Battjes et al. (2003) the bound wave travelling shoreward is observed to grow faster than Green's Law, indicating that the bound wave gains energy from other spectral components. Under certain conditions, specifc low-frequency components show growth equal to the equilibrium response, as was presented by Longuet-Higgins and Stewart (1962). In addition to the above observations, laboratory experiments were performed. The observations are compared with an energy model transfer model enabling energy transfer from high frequency waves (HF) to low-frequency waves. To obtain quasi-continuous estimations of the bound wave amplitude, high resolution 2-D laboratory data is obtained for several (both bound wave frequency varying and modulation varying) bichromatic and irregular wave fields. The test were performed on a plane sloping (1:35) beach. Based on existing models concerning surfbeat generation a testprogramme is designed to determine a criterion for the beach slope being 'gentle' or 'steep' for long wave frequencies. The analysis of the acquired data comprises long wave decomposition into incoming and outgoing waves. The decomposition method presented by Bakkenes (2002) is extended with two iteration steps. Phase analysis of the incoming bound wave and incoming HF wave groups shows an increasing phase lag of the bound wave after the wave groups. This phase lag is used in the energy transfer model. Comparison to the predicted values of the model with (decomposed) observations shows very good agreement for the incoming LF waves, but large deviations for the outgoing LF waves. Furthermore, the amplitude growth of the incoming bound long wave is compared with the 'equilibrium response growth' and related to the normalized bed slope as an indication whether the equilibrium response is to be expected. From the present observations it is concluded that a lower value of the bed slope gives a good indication for the energy transfer rather than for the amplitude growth; for higher subharmonic frequencies signifcant energy dissipation occurs, preventing the LF wave to grow as expected based on the bed slope variation. The varying modulation does not lead to different amplitude behavior. The outgoing wave amplitude is observed to be highly dependent of the bound wave frequency. In specific cases, the outgoing amplitude exceeds the incoming amplitude. No conclusions are drawn concerning the processes governing the reflection.