Influence of uniform currents on nonlinear characteristics of double-wave-group focusing

The linear superposition of the individual wave groups underestimates the bimodal waves, as it overlooks the interactions between these wave groups, which is thought to be connected to the generation of extreme waves. Continuing our previous work [Zhou et al., “Experimental study on the interactions between wave groups in double-wave-group focusing,” Phys. Fluids 35(3), 037118 (2023)], the energy transfer in the spatial evolution of double-wave-group focusing is highlighted based on a fully nonlinear numerical wave tank with the high-order spectral method. The findings reveal that a sea state with a narrower intermodal distance or an uneven distribution of the bimodal spectrum tends to induce larger waves. The third-order nonlinear interaction is primarily triggered by the transient wave focusing, as opposed to a prolonged evolution like the behavior of even-order components. The configurations of the sea state exert varying impacts on the evolution of harmonical energy, with the most potent nonlinearity observed away from the actual focused position, the nonlinear energy amplified relative to the initial state, and the energy redistributed after wave focus. The study also uncovers that during the wave focus and defocus process, waves experience an irreversible energy exchange, with frequencies shifting from higher to lower, likely due to second-order harmonics. These discoveries broaden our comprehension of the nonlinear characteristics inherent in the interaction between the swell and wind-sea waves.

Energy transfer in the spatial evolution of double-wave-group focusing

Zhou,

Ding,

Xiao

et al. 2024

Spatial evolution of the double-wave-group focusing influenced by the co- and counter-propagating current

Ding,

Zhou,

Xiao

et al. 2024

Wave–current interaction has always been a challenging topic in fluid mechanics. The research on bimodal waves has received much more attention recently, but their evolutions influenced by underlying currents are not yet clear. This study aims to investigate the effects of co- and counter-propagating currents on spatial evolution using a fully nonlinear wave-current tank based on the high-order spectral method. The process of the wave focus is significantly shortened by the counter-propagating current, resulting in a sharper crest focus, followed by the trough focus. Concurrently, the decrease in the total envelope height and width is accelerated before wave focus and then the increase is decelerated, accompanied by a delay in the envelope profile transition from the backward-leaning to the forward-leaning. The co-propagating current exhibits the opposite phenomenon. The analysis of the spectral energy distribution aids in clarifying the variation of the envelope profile. The energy redistribution, characterized by a downshift of the frequency band, and a decreased energy distribution at the second peak, along with the slightly larger value of the root mean square frequency, indicates that the energy back-flow is obstructed by the counter-propagating current. These findings contribute to our understanding of the current effect on the focused double-wave-group, providing valuable insights for future research and applications in this field.

The steady-state solution of wave–current interaction based on the third-order Stokes wave theory

Ni,

Wei,

Luo

et al. 2024

This manuscript reports on the interaction of a current-free monochromatic surface wave field with a wave-free uniform current field. The existing reasonable theories of wave–current interactions are primarily based on weak current assumptions and derived from linear theory, resulting in calculation bias in the analysis of nonlinear wave–current interactions. Moreover, experimental data on high-order wave–current interactions still need to be collected. Thus, steady-state solutions named the third-order wave–current theory based on the third-order wave dispersion relationship and the principle of wave–current energy conservation were derived. The wave–current interaction experiment was set up to cover 164 sets of experimental conditions, including 33 types of periodic waves from the second to the fifth order and six different current velocities. The effects of water depth, current velocity, wave period, and height on the wave height and wavelength in the wave–current interaction field were investigated. A comparison of the mean relative error (MRE) and the determination coefficient (R2) of the wavelength with the experimental data revealed that the third-order wave–current theory outperformed the traditional linear theory, with an optimal reduction of 75% and an enhancement of 25%, respectively. Additionally, the third-order wave–current theory reduces the MRE by 25%–40% in the wave height calculation, with R2 consistently outperforming the linear theory. The third-order wave–current theory can significantly improve the calculation accuracy of the theoretical method in solving nonlinear wave–current interactions.