An experimental comparison of the velocities and energies of focused spilling waves in deep water

It is important to achieve a better understanding of the wave energy variations occurring as a steep wave evolves towards breaking. Laboratory experiments of focused waves are performed to investigate the kinematics of primary breaking waves. When a primary wave evolves towards breaking, the increase in the maximum kinetic energy is stronger than the increase in the maximum potential energy. Furthermore, the accuracy of the average energy of the wave train analyzed by the wave spectrum is discussed. At measuring locations far from the breaking onset point, the average energy of the wave train analyzed by the wave spectrum is slightly larger (0.6–2.5%) than the average energy calculated by the measured free-surface elevation and fluid velocities. In contrast, at measuring locations close to the breaking point, the nonlinearity of the wave train is strong and the average energy analyzed by the wave spectrum underestimates the measured wave energy. The error ranges of the total energy loss rate of deep-water wave breaking calculated by wave spectrum analysis are 1.5–3.79% and ±1.9% for measuring locations close to and far from the breaking point, respectively. Although the absolute value of the error is not prominent, the error range is not negligible relative to the energy loss rate of a single spilling wave. Finally, a wave index ϵ ∗ ( f s / f p ) is proposed to reveal the characteristics of the wave energy variations during the incipient breaking stage under different wave conditions.