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 dataset, 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 that exceed twice the significant wave height indeed 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 dataset 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 dataset from the southern North Sea. Significance Statement This work investigates whether rogue waves measured in the southern North Sea may have been generated by a modulational instability. The latter is a nonlinear mechanism of wave energy focusing that has been proven mathematically and confirmed in laboratory experiments. However, it is still unclear whether this mechanism is responsible for rogue wave generation under realistic ocean conditions. The modulational instability primarily arises when waves have similar frequencies and directions. In our data, these conditions were not satisfied. This finding leads to the insight that the modulational instability is not the most probable mechanism to generate rogue waves in our dataset.