Laboratory experiments on waveform inversion of an internal solitary wave over a slope-shelf

Abstract

Internal solitary waves (ISWs) have been detected in many parts of the world oceans, particularly over slope-shelf topography, on which signature of waveform inversion has been identified. The effects of these waves on engineering operations and ecological process have also been reported in the literature. This article reports the results of a series of numerical modeling and laboratory experiments on waveform evolution of a depression ISW in a nearly stratified two-layer fluid system, in which specific water depth ratios above the horizontal plateau of the trapezoidal obstacle were arranged to facilitate the occurrence of waveform inversion. Classifications of waveform instability (no instability, shear instability and overturning with breaking) on the slope are confirmed in the present laboratory study. Numerical results for waveform variation are also found in fair agreement with the laboratory measurements for cases without waveform inversion and minor internal breaking. Moreover, laboratory results revealed that the depth ratio of the stratified two-layer fluid above the plateau and the magnitude of the incident ISW were the two most important factors for promoting waveform inversion beyond a turning point, in addition to the requirement of a sufficient distance from the shoulder of the trapezoidal obstacle. These factors also influenced the outcome of the shoaling process, energy dissipation, internal wave breaking and turbulent mixing on the front slope, as well as the likelihood of waveform inversion on the horizontal plateau. Contrary to the common perception, it was also observed, at least from the results of the present laboratory experiments, that not all the incident ISWs of depression would produce waveform inversion on the plateau, where the upper layer was physical greater than the bottom layer, unless moderate incident wave was provided. The outcome might also be attributed to the limited distance from the shoulder onto the plateau in the present laboratory setup. However, once waveform inversion occurred on the plateau, it was found, among others, that: (1) the amplitude of the transmitted leading crest and trough might be as low as 30 and 20%, respectively, to the amplitude of the incident wave in depression; (2) the characteristic wavelength of the transmitted leading trough doubled while that of the crest was asymptotically one-half of the incident wavelength, despite the wide range variation in the depth ratios above the plateau; and (3) the transmitted potential wave energy of the leading crest contained 30% of the incident energy. Based on the results of present laboratory experiments, the range for the non-dimensional parameter α, which indicates the effect of nonlinearity and the promotion of waveform inversion on horizontal plateau, will be proposed.