On the Characteristics of Randomness, Nonlinearity and Energy Dissipation of Wind Wave Breaking
|School||Ocean University of China|
|Keywords||wind wave breaking stochastic point process bispectra energy dissipation breaking criteria|
Wind wave breaking in deep water is an important component in the process of air-sea interaction, playing a primary role in the exchange of mass, momentum and energy between the atmosphere and the ocean, which have a profound effect on weather and climate. It serves to maintain the energy balance within the continuous wind-wave field and limit the height of surface waves, mix the surface waters, generate ocean current. Its role in the dynamics of the upper ocean is critical.However, it may represent one of the most complex physical phenomena of nature. It is an intermittent random process, with strong non-linearity, very fast by comparison with other processes in the wave system, and the distribution of wave breaking on the water surface is not continuous. The intermittency and randomicity of the wave breaking are the main barriers in the breaking wave research. Due to lack of proper mathematical representation, they are not clear for us by now.Actually, the intermittency and randomicity can be clearly described by stochastic point processes. The concept and theory of stochastic point process were introduced into wave breaking research. Wind wave breaking observed at a fixed point can be viewed as a one-dimension point process; considering the groupness of breaking waves, cluster point process is the general model for wind wave breaking; marked point process is proper for the expressing energy loss due to breaking. In this theoretical frame, definition and estimation of breaking probability and energy dissipation were discussed strictly. Breaking probability is the mean of a stochastic process and the energy loss due to breaking is a stochastic processes. A series of wind wave breaking experiments and the data analysis results reveal that the theory and method of stochastic point process is effective for wind wave breaking research. This is a new way to understand wind wave breaking.The bispectrum can measure the non-linearity of a process, and wind wave breaking is a process with strong non-linearity. The bispectra of breaking wind waves under different breaking rate were investigated and come into the following conclusions:the maxima and the integral of the real part of wind wave bispectra, and the skewness of the wave elevation time series increase with dominant wave breaking probability sensitively, and they are suitable for measuring the breaking frequency, however, there is no clear trend in the maxima and the integral of the image part of bispectra at different wind speed.Energy dissipation due to wave breaking is a focus of the breaking wave research, and there is much difficulty in it. A brief review of breaking dissipation research was presented and two methods for estimating the energy loss of breaking wave were inspected. Young and Babanin (2006) separate the surface waves into two categories: breaking segments and non-breaking segments, the difference between "breaking spectrum" and "non-breaking" spectrum was attributed to the dissipation due to breaking. Yefimov and Khristoforov (1971a) use the difference of the measured velocity spectrum and the wave-induced spectrum as the estimated energy dissipation. Results from our data analysis using first method are reasonable but the other is not.Reliable breaking criterion is needed in our research, so the classical breaking criteria for surface elevation time series were investigated. Variables for kinematics criterion and for dynamic criterion and instantaneous wave slope are all sensitive to the breaking events, and well consistent in distinguishing the breaking waves. Those geometric variables such as wave steepnees are not so good.Based on the data of wind wave experiments, using dynamic criterion, the breaking wave and breaking groups were determined, the sequences of time interval between breaking waves and sequences of the number of breaking waves in a group were obtained. The stochastic point process theory for wave breaking was demonstrated as following:The intermittency of wind wave breaking can be clearly described using the distribution of the intervals between breaking wave. There is a common feature is that the proportion of small intervals is large and those of large intervals are small. The Kolmogorov-Smirnov test for interval sequences show that the probability distribution for intervals between breaking waves in lower wind speed is exponential distribution. This indicates that, in the lower wind speed case, the breaking waves formed a homogenous Poisson process. Correspongingly, the cumulated marked process for breaking dissipation can be simplified into compound Poisson process.In the higher wind speed case, groupness is the distinct character of wind wave breaking. The groupness of wave breaking can be expressed by the distribution of the number of breaking waves in a group. The groups containing more than one breaking wave occurred only when wind speed come up to certain level. The higher the wind speed is, the more of such groups, and the large is the averaged number of breaking waves in a wave group.The breaking rate is near with the reciprocal of the averaged breaking interval. In fact, the dominant wave breaking probability, breaking rate, the reciprocal of the averaged interval between breaking waves and the averaged number of breaking waves in a wave group are highly correlated in linear way, they are one kind of index for measuring breaking frequency, the group breaking probability, group breaking rate, and the averaged interval between breaking groups are the other kind of breaking frequency index. It is much better to combine these two kind indexes when describing how frequently the breaking is.