On Determining the Onset and Strength of Breaking for Deep Water Waves. Part II: Influence of Wind Forcing and Surface Shear

Abstract

Part I of this study describes the authors' findings on a robust threshold variable that determines the onset of breaking for unforced, irrotational deep water waves and proposes a means of predicting the strength of breaking if the breaking threshold is exceeded. Those results were based on a numerical study of the unforced evolution of fully nonlinear, two-dimensional inviscid wave trains and highlight the fundamental role played by the nonlinear wave group dynamics. In Part II the scope of these calculations is extended to investigate the additional influence of wind forcing and background shear on the evolution to breaking. Using the methodology described in Part I, the present study focuses on the influence of wind forcing and vertical shear on long-term evolution toward breaking or recurrence of the maximum of the local energy density within a wave group. It investigates the behavior of a dimensionless local growth rate parameter that reflects the mean energy flux to the energy maximum in the wave group and provides a clearer physical interpretation of the evolution toward recurrence or breaking. Typically, the addition of the wind forcing and surface layer shear results in only small departures from the irrotational, unforced cases reported in Part I. This indicates that nonlinear hydrodynamic energy fluxes within wave groups still dominate the evolution to recurrence or breaking even in the presence of these other mechanisms. Further, the calculations confirm that the breaking threshold for this growth rate found for unforced irrotational wave groups in Part I is also applicable for cases with wind forcing and shear typical of open ocean conditions. Overall, this approach provides an earlier and more decisive indicator for the onset of breaking than previously proposed breaking thresholds and suggests a foundation for predicting the strength of breaking events.