Comprehension of the statistical distribution of steep and breaking surface waves is crucial to the understanding of such issues as the air-sea momentum flux and the airsea gas exchange. My work, begun in January 2004 and funded by CICOR, is aimed at understanding the distribution of steep surface waves that are part of steep wave groups on the ocean surface. This is accomplished through the use of a new signal processing algorithm based on wavelet analysis. This methodology is applied to open ocean wave height data acquired from wave gauges during the Flux, Etat de la mer et Teledection en Condition de fetch variable (FETCH) experiment (1998) and the Adverse Weather Experiment (1998). Both experiments were air-sea interaction studies which employed the use of the Air-Sea Interaction Spar (ASIS) buoy, a spar-buoy designed specifically for the measurement of directional wave spectra and meteorological parameters.
Wavelet analysis of ocean surface wave data yields a quantity dubbed the steep wave statistic. The steep wave statistic,NT (k,θ) T , is simply the number of steep wave crests at wave slope threshold T, wavenumber k, and angle θ It is calculated via a two part process. First the wavelet transform is used to not only detect local steep wave events which pass over a wave gauge array but also to find their scale. These events are tallied up according to wavenumber, angle, and wave slope threshold to yield the statistic.
Results from the analysis of wave gauge measurements of the surface wave field from the Adverse Weather experiment and the FETCH experiment are shown in Figure 1. The figure shows NT , the average number of steep wave events at wave slope threshold T versus wavenumber k . The wave slope thresholds are listed in black with increasing wave slope threshold from top to bottom corresponding to each of the curves of decreasing mean value for NT . The figure shows that high wave slope crests appear ove a wide range of wavenumbers for both the low wind case and the high wind case. Figures 1a and 1b show that at low wave slope thresholds, a larger amount of steep waves at low wavenumbers exists than at high wavenumbers. As the wave slope threshold is increased, the trend changes with the number of steep waves increasing with wavenumber, over a large portion of the wavenumber range. These curves point to the importance of the small-scale steep waves in characterizing the wave field. Comparison of Figure 1a to Figure 1b shows that the trend at high wave slope thresholds is modulated in the case of high wind with the slope of the curves being gentler than in the previous case. This may be due to the presence of very steep and breaking waves in the wave field which occur at high wind speeds.
Directionality analysis of the waves was also performed. Figure 2 depicts the steep wave angular distribution, NT for two different experiments as a function of angle, θ where the direction of the wind is at zero degrees. The plots show that irrespective of wave slope threshold, most of the steep waves move in the mean wind direction. This is qualitatively consistent with other observations.
The complete form of this work is in preparation for publication in Elsevier Scientific’s Applied Ocean Research.