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

Abstract

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.