Researchers from the Ruhr- Universität Bochum and the University of Umeå, Sweden say they have developed a new statistical model for non-linear, interacting waves in computer simulations which will allow them to be theoretically calculated and modeled.
They say their model explains how the water-wave system evolves, behaves and, above all, how it stabilizes itself. They say their model is also suitable for the calculation of other 'extreme occurrences - yes, more numerical models by physicists on the stock market, because we have seen how well that works - or more complex phenomena in plasma physics. Bochum’s physicist Prof. Padma Kant Shukla and his Swedish colleague Prof. Bengt Eliasson report on their findings in Physical Review Letters.
Shukla and Eliasson simulated how the giant freak wave occurs four years ago. If two or more waves meet at a certain relatively small angle, they can progressively “amplify” each other. Two non-linear interacting waves therefore act very differently to a single wave which shows normal instabilities and breaks up into several small waves, which then run diagonally to each other. Two non-linear waves, however, cause the water to behave in a new way, for example, the emergence of downright “wave packets” with amplitudes three times higher than that of a single wave. Buoyed by strong currents and powerful – opposing – winds, the giant wave can continuously build up from there.
With their new statistical model, they say they have succeeded in taking another crucial step towards explaining this freak wave: it results from combined non-linear effects in the wave-to-wave interaction and the dispersion of the “wave packets” in a certain direction.
This causes the energy of the water to be concentrated “in a narrow band across a confined wavelength spectrum”, and with sudden, large amplitude. The actual instability of individual waves is “saturated” through the broadening of the wave spectrum, thus the water-wave system temporarily stabilizes itself.
This behavior is typical for the localized giant wave, the researchers explain. Their calculations tally with observations from experiments in large water tanks. “These show that long-crested water waves, i.e. groups of waves propagating in approximately the same direction, have an increased tendency to evoke extreme events,” said Shukla and Eliasson.
A step towards prediction
Since the cruise liner Queen Elizabeth 2 encountered a freak wave in 1995, giant freak waves have been a source of study, finally being outside mariner 'tall tales'. The damage to passenger and cargo ships and also oil platforms at sea can be considerable. Shukla and Eliasson’s statistical model may lead to predicting freak waves in certain regions, such as the North Atlantic or the Mediterranean, and provide early warning in future. The deeper physical understanding of the giant wave and statistical calculation would have to be combined with new, improved methods of observation, the researchers say.
Citation: Bengt Eliasson and P. K. Shukla: Instability and Nonlinear Evolution of Narrow-Band Directional Ocean Waves. Physical Review Letters 104, Editor: Jens Wylkop. DOI: 101103
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