On The Breaking Of Energetic Waves

The historical development of attempts to understand and quantify the breaking of energetic gravity waves is reviewed, and some new theoretical results are presented. The importance of at-sea observations, and of the appearance of wave breaking near the center of wave groups is emphasized. Discrepancies between laboratory measurements of wave steepness at breaking, (H/gr)* = 0.021, and recent measurements at sea, (H/gT2)*avg = 0.0067 are explained in terms of the fetch dependence of the breaking of modulated waves, as shown experimentally by Su and Green (1984). With regard to mechanism, the role of non-linear resonant wave interactions leading to modulations, and of wave deformation is stressed. Finally we outline a new theoretical analysis of the breaking mechanism, central to which is the role of resonant (sideband) instability as an intermediary mechanism for rapid wave deformation leading to breaking within wave groups. Results are shown to be in excellent agreement with observational laboratory experiments of Bonmarin (1989) and observations of breaking in wave groups at sea. surements at sea. Much of the research is exploratory (i.e., fact finding), and the various efforts have not been well-coordinated. A special difficulty is the ambiguous relation between controlled experimental studies, and measurements at sea. For example, there has been no systematic study of the effect of scale on breaking, nor is it yet entirely understood which aspects of real sea waves are crucial to an understanding of breaking (i.e., wind, currents, spectral shape, directionality, etc.). Despite these difficulties, as we show, comprehension of at least one important breaking mechanism for energetic waves may be within our grasp. For that we have to understand wave instability and non-linear wave interactions. We begin with a brief and selective review of the search for a breaking criterion in terms of wave steepness, or other simple local conditions. Here we show that neither the idea of a limiting wave steepness nor widely accepted laboratory values of limiting steepness, (H/gT2)* = 0.021, are in accord with measurements at sea. We explain this discrepancy in terms of the fetch dependence of breaking inception for waves of varying steepness, as shown by Su and Green (1984). Finally a picture begins to emerge that is consistent with available laboratory and sea observations, not the least of which is the tendency of waves to break at sea within wave groups. Central to this picture is the role of resonant (sideband) instability as an intermediary mechanism for wave deformation leading to breaking within wave groups. Finally we outline a new theoretical analysis of this intermediary mechanism; this allows calculation of the deformation and the time rates involved, which are shown to be in excellent agreement with observational laboratory experiments of Bonmarin (1989). Other conclusions are drawn that are in accord with observations. INTRODUCTION Those long waves spread under the peak in the energy spectrum are of greatest concern for the safety of ships and marine structures, and coming inshore for the integrity of the shore environment. Furthermore, at-sea measurements of breaking waves show that the breaking waves are about twice as energetic as the wave of mean height (Holthuijsen and Herbers, 1986). Here we review our understanding of the breaking of these energetic waves at sea in deep water. We have the advantage that they are predominantly long-crested, so that we can approximate them, at least prior to breaking as planar waves. Breaking is itself characterized by a forward motion of the crest, a steepening of the forward face of the wave, and an accompanying increase in the water velocity at the crest, q*. From everything we know, when q* becomes as large as the wave celerity, c, then the irreversible overturning process becomes inevitable (Fig. 1). Therefore, this condition, q* ~ c, is a good criterion to separate breaking and nonbreaking waves in practice; Melville and Rapp (1988), in a tank experiment using a laser velocimeter, have proven this criterion and have shown that wave height itself, or even rapid rises in wave height, cannot distinguish breaking waves without error. Upon observing breaking waves in deep water, it is natural to ask: Why do sea waves break? What is the hydro-mechanics? Are there appropriate criteria for the inception of breaking? How can we model the breaker as it evolves? Although the subject is 140 years old and great progress has been made in recent decades, these large basic questions still remain largely unanswered. That is why the fundamental study of breaking waves is so challenging. As we shall see, our current knowledge of breaking is derived from a combination of: theoretical analysis and computation, controlled experimental studies, and actual observations and meaReceived June 24, 1991: revised manuscript received by the editors February 5, 1992. The original version (prior to the final revised manuscript) was presented at The First International Offshore and Polar Engineering Conference (lSOPE-91), Edinburgh, United Kingdom, August 11-16, 1991.