Rogue Waves in the Southern North Sea-The Role of Modulational Instability

Abstract

The role of the modulational instability for rogue wave generation in the ocean is still under debate. We investigated a continuous data set, consisting of buoy and radar wave elevation data of different frequency resolutions, from eight measurement stations in the southern North Sea. For periods with rogue waves, we evaluated the presence of conditions for the modulational instability to work, that is, a narrow-banded wave spectrum in both, frequency and angular direction. We found rogue waves exceeding twice the significant wave height indeed to occur at slightly lower frequency bandwidths than usual. For rogue waves that are defined only by high crests, this was, however, not the case. The results were dependent on the measurement frequency. The directional spreading of the buoy spectra yielded no information on the presence of a rogue wave. In general, all spectra estimated from the data set were found to be broad in frequency and angular direction, while the Benjamin–Feir index yielded no indication on a high nonlinearity of the sea states. These are unfavorable conditions for the evolution of a rogue wave through modulational instability. We conclude that the modulational instability did not play a substantial role in the formation of the rogue waves identified in our data set from the southern North Sea.