Calculation of the Accelerated Breaking-Roller Propagation Speed and Wave Energy Transfer to the Roller

Wave breaking has different physics from the potential flow wave motion. The roller model introduced by Svendsen [1] illustrates the separation of the wave motion and the roller. The roller propagation speed, therefore, is a very important factor for the energy calculation of the bore. The wave celerity data collected at the wave tank displays that the maximum roller propagation speed occurs when the wave has already decayed due to the breaking. This fact clearly displays that the bore energy cannot be calculated only from the wave height as it is done for non-breaking waves. It is certain that most the energy is dissipated through the roller formation in the outer surfzone, but a certain amount of energy is transferred to the roller at the same time and it accelerates the bore speed. Slow decay of the roller propagation speed indicates that the excess energy left in the roller dissipates in the inner surfzone at much slower rate than in the outer surfzone. Therefore, these two zones have to be clearly separated, but the amount of energy transferred into the roller is unknown. In this paper, we focus on the examination of the peak roller propagation speed that appears at the border of the outer and the inner surfzone by using the experimental data collected at the wave tank. In that way, the initial condition of roller propagation speed can be determined for the inner surfzone. The energy conservation between the wave motion and the roller kinetic energy derives an equation to calculate the roller propagation speed. The energy transfer rate is estimated by adjusting the value given by the full energy conversion with the observed roller propagation speed. It is found that about half of the energy is transferred into the roller. The model successfully illustrates the peak bore propagation speed which existing formulae cannot explain.