Laboratory investigation of turbulence scales of swash flows generated by consecutive solitary waves

Using direct spatial spectrum and continuous wavelet transform analyses, turbulence scales in the swash flows, generated by six consecutive solitary waves in the laboratory, are examined. This study focuses on the interactions between uprush flows and downwash flows under two different incident wave conditions. Because the spatial resolution in the experimental data is limited, the direct spatial spectral method can only provide meaningful information in the region with larger turbulence length scales, which is of the order of the integral length scale in the energy cascade of the turbulent kinetic energy spectrum. In the present experiments, the integral length scale is found to be as large as the local water depth (1 to 3 cm). Since the temporal resolution of the experimental data is high, the continuous wavelet transform is employed to investigate the smaller turbulence length scale region within the inertial subrange by invoking the Taylor-frozen hypothesis. The results reveal that the slope of the time-dependent energy cascade changes rapidly, showing that the exchange of turbulent kinetic energy across the length scales occurs through the inverse cascade, the downward cascade, and the typical $-5/3$ slope cascade for turbulent flows. The $-3$ slope of the energy cascade occurs due to the bed-generated eddies when the nonstationary hydraulic jump develops. The energy cascade with $-1$ slope occurs at the flow reversal from the downwash to the uprush at which the broken bore develops. The typical slope $-5/3$ occurs during the uprush flow. Taking the time average of the time-dependent spectrum obtained by the continuous wavelet transform method, an overall slope of $-1$ is found across multiple energy bumps throughout the inertial subrange of the energy cascade for the two interacting wave conditions.