Observations of Rogue Seas in the Southern Ocean

We report direct observations of surface waves from a stereo camera system along with concurrent measurements of wind speed during an expedition across the Southern Ocean in the austral winter aboard the South African icebreaker S.A. Agulhas II. Records include water surface elevation across a range of wave conditions spanning from early stages of wave growth to full development. We give experimental evidence of rogue seas, i.e., sea states characterized by heavy tails of the probability density function well beyond the expectation based on bound mode theory. These conditions emerge during wave growth, where strong wind forcing and high nonlinearity drive wave dynamics. Quasiresonance wave-wave interactions, which are known to sustain the generation of large amplitude rogue waves, capture this behavior. Wave statistics return to normality as the wind forcing ceases and waves switch to a full developed condition.

Figure 1

Ship track [yellow lines; (a)] and sample images (b),(c): example of overlapping stereo images (b) and reconstructed three-dimensional surface (c).

Figure 2

Evolution of spectral characteristics across different stages of wave growth as measured by the wave age: (a) wave steepness (symbols) and frequency bandwidth (color map), (b) directional spreading (symbols) and directional spreading relative frequency bandwidth (color map), and (c) two-dimensional Benjamin-Feir Index. Examples of sea state images at different wave age are reported: (d) growing (young) sea state ($C_P/U\approx 0.5$), (e) near fully developed sea state ($C_P/U\approx 1$), and (f) a fully developed sea state ($C_P/U\approx 2$).

Figure 3

Field observations of the kurtosis of the surface elevation as a function of the wave age. Estimates of the maximum wave crest based on a fitted three-parameter Weibull distribution are reported as a color map. The (light blue) shaded area is shown to identify values of kurtosis normally expected for Gaussian and weakly non-Gaussian sea states. A comparison against theoretical predictions based on bound and free wave contributions is shown in the inset. The error bars represent the 95% confidence interval.

Figure 4

Wave crest distribution in young [$C_P/U\approx 0.5$; (a)] and fully developed [$C_P/U\approx 2$; (b)] sea states from in situ data and theory [9]. Comparison of maximum wave crest amplitudes extrapolated from in situ data and theoretical [9] distributions (c).

Figure 5

Probability density function of the normalised wave intensity ($P_N$) for a young (a) and mature (b) seas; the 99% confidence interval is indicated as shaded (light blue) area. The young sea represents data from a sequence of images acquired for wave age $C_P/U\approx 0.5$; the mature sea represents data from a sequence of images acquired for wave age $C_P/U>1$. The $\exp (-P_N)$, which represents a Gaussian process, is reported for a benchmark.