Long waves in the North Sea: Distribution, generation and measurement methods

This report presents the results of a research concerning long waves in the North Sea. ‘Long waves’ in this research is a collective name for various types of waves that are longer than the well-known sea-swell waves, here referred to as ‘short waves’. Wave types that are referred to as long waves are infragravity waves, meteo-tsunami’s, seiches and tides. Besides their extensive length, they distinguish themselves from regular sea-swell waves by the mechanisms responsible for their generation and the scale of their impact. Whereas short waves are generated by wind, long waves are generated by short wave-group forcing, the breaking of short waves nearshore and large atmospheric pressure variations. Long waves play a crucial role in the processes of coastline erosion and the breaching of flood defenses, as well as in the formation of rip currents and seiches. These events can lead to severe damage to hydraulic structures and possibly even casualties. A better understanding of them is thus vital for coastal safety. Rijkswaterstaat has been collecting data regarding the occurrence of long waves on the North Sea for over a decade. Their measurement campaign started in a time when digital broadcasting signals and digital storage space were not well developed yet, making sending and storing the water surface elevation time-series not feasible. The data is therefore filtered by a FIR filter, reducing the size of the data, but also reducing the information that is contained in the data. All frequencies of approximately 0,0125 퐻푧 and higher are removed by the FIR filter. As a consequence a significant part of the infragravity signal is missing and it is not possible to perform a bispectral analysis (used to determine the bound long wave contribution). Nowadays, digital broadcasting signals and digital storage space have plenty of capacity to send and store the data, making the filter unnecessary. Analysis of the spatial- and temporal distribution of long waves in the North Sea, shows that the majority of long waves have a yearly averaged significant wave height of 2,4 - 3,3 cm and a yearly averaged mean wave period of 125 to 140 cm. Based on data from the full decade, a clear trend in the spatial distribution of long waves cannot be distinguished, offshore and nearshore locations show approximately the same long wave properties. The seasonal analysis shows that the mean significant long wave height averaged out over all locations per season varies from 2,8 cm during summer, 2,9 cm during spring, 3,3 cm during winter to 3,5 cm during fall. For the mean wave period, the mean value averaged out over all locations per season varies from 127,5 s during summer, 128,1 s during spring, 135,6 s during winter to 136,3 s during fall. Predictions of the extreme wave conditions show that the significant wave height with a return period of 10.000 years (Dutch design condition for coastal flood defenses) are around 40-60 cm, although there is quite some uncertainty in these predictions. This uncertainty is due to a relatively short measurement period, usually 30 years of data is used for extreme wave predictions, and remarkable observations in the data. Time-series analysis of the hourly significant wave height of long waves and predicted bound long waves (Hasselmann, 1962) (Hasselmann, 1963) shows that during mild weather conditions significant wave heights of long waves are low, with minimal contributions by the bound long waves. At the onset of a storm, the significant wave height of both long waves and bound long waves rapidly increase. At the end of the storm, they decrease to the pre-storm values. This shows that the generation of long waves occurs mainly during heavy weather conditions. Hourly significant wave heights of long waves, and especially bound long waves, show a strong correlation with significant short wave heights. The relative contribution of bound long waves (퐸푏푙푤/퐸푙푤) during a storm increases up to values of 60%, which is considerably higher than contributions of bound long waves found in other studies (Herbers et al., 1994). The high ratio of the relative bound long wave contribution, in combination with very low bound long wave activity during mild conditions, shows that the generation mechanism involving wave-group forcing is a major generation mechanism of long waves in the North Sea.