Modulational instability and wave amplification in finite water depth

Abstract

Abstract. The modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates the instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative depths kh ≤ 1.36 (where k is the wavenumber of the plane wave and h is the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for kh ≤ 1.36. Results, nonetheless, indicate that modulational instability cannot sustain a substantial wave growth for kh < 0.8.

Laboratory investigation of crest height statistics in intermediate water depths

“…By contrast, field data from Lake George, Australia included in the same study indicate notable amplifications beyond the second-order crest height statistics in the steepest sea states. Additionally, experimental and numerical studies [38,39] of idealized wave groups have shown that instabilities can develop due to oblique perturbations; the theoretical basis having been provided by Hayes [40]. These latter results are important, not least because the analysis of field data from intermediate water depths has confirmed the existence of both unexepectedly large wave crests [41,42] and crest height distributions departing from second-order theory [43,44].…”

HOS-ocean: Open-source solver for nonlinear waves in open ocean based on High-Order Spectral method

“…In this section, the High-Order Spectral method used in HOS-ocean code is presented. HOS models have been widely used for the study of wave propagation in open domains starting from the original work of [31] & [8] up to the analysis of complex wave phenomena [27,28,29,16], including freak waves [12,32,24], among others. Extensions of the original HOS model to include wind forcing effects [30,19] and jet current effects [25] are also worth to mention.…”

“…HOS models have been widely used and validated by several authors to study different physical mechanisms: e.g. in recent years nonlinear energy transfers [27], modulational instabilities [16], [28], bi-modal seas [29], freak waves [12,32,24] . .…”

On the equivalence of unidirectional rogue waves detected in periodic simulations and reproduced in numerical wave tanks

“…HOS models have been widely used for the study of wave propagation in open domains starting from the original work of [42] & [13] up to the analysis of complex wave phenomena [35,38,39,19], including freak waves [15,43].…”

“…Several physical phenomena have been studied thanks to this highly nonlinear model, e.g. non-linear energy transfers [35], modulational instabilities [19,38], and bi-modal seas [39] among others.…”