Spatial and Temporal Characteristics of Transient Extreme Wave Profiles on Depth-Varying Currents

Abstract

The results of laboratory experiments on transient (short lived), extreme (highest nonbreaking) waves on depth-varying currents are reported. A new feedback control wave focusing method on currents was developed to create transient, extreme waves in the presence of desired depth-varying currents at the prescribed position. Both wave profiles and time series of surface displacements were measured to examine the spatial and temporal characteristics of extreme waves. Wavelengths estimated from dispersion relations consistently underestimated those measured directly from the video images of transient extreme waves. This underestimation well correlates with a proposed wavelength asymmetry parameter ξ (a ratio of the trough length to the crest length), suggesting the rapid change of a transient wave profile during a wave cycle. The effects of the current shear on transient, extreme wave profiles are recognized. The negative shear increased the limiting wave steepness but reduced the vertical asymmetry. The vertical asymmetry could be remarkably augmented by the positive current shear, while the limiting wave steepness was reduced. These results were clearly observed in the spatial wave profiles, but not in the time series of the surface displacement.