New model describes wave behavior in straits, predicts killer waves

A Skoltech researcher has developed a theoretical model of wave formation in straits and channels that accounts for nonlinear effects in the presence of a coastline. This research can improve wave prediction, making maritime travel safer and protecting coastline infrastructure. The paper was published in the journal Ocean Dynamics.

Predicting surface weather at sea has always been a challenging task with very high stakes; for instance, over 4,000 people died due to rough seas during Operation Overlord at Normandy in June 1944, an allied incursion where poor forecasting altered the course of the operation quite significantly. Current wave forecasting models used, for example, by NOAA in the US, are imperfect, but they have many tunable parameters to ensure a reasonably good prediction.

However, as Andrei Pushkarev, senior research scientist at Skoltech and Lebedev Physical Institute of the Russian Academy of Sciences notes in his paper, coastlines complicate the situation: he writes that, “wave forecasting in the English Channel nowadays is still almost as hard as it was in 1944.” His research suggests that the wave behavior in channels or straits will differ quite significantly from that in open seas.

“Coastlines create inhomogeneity – a gradient of the wave energy distribution between its zero value at the boundary and non-zero value off-shore. This gradient launches wave advection, and its mutual interplay with nonlinear wave interaction creates peculiar effects of generating waves orthogonal to the wind,” Pushkarev says.

The specific conditions of the channels allow for a precise solution of the Hasselmann equation describing wave behavior, the one current models approximate because it is still impossible to solve with modern computers. Pushkarev’s theoretical modeling of wave formation in an English Channel-like strait showed that the development of turbulence did not match predictions from conventional models, as turbulence structure was significantly different due to nonlinear interactions and wave advection. Since the phenomenon researchers observed has some similarities to laser radiation, they call it the Nonlinear Ocean Wave Amplifier, or NOWA. 

“The strait shores play the role of the semi-reflecting mirrors for generated waves, which makes the situation similar to conventional lasers, with the nonlinear wave media playing the role of active resonator, in some sense similar to the conventional lasers. The power of the radiation excited orthogonally to the wind grows significantly with the growth of the reflection coefficient of the strait boundaries. In a sense, we are dealing with some sort of nonlinear laser,” Pushkarev notes. 

“This model, exploiting the exact version of the Hasselmann Equation, shows that existing operational wave weather forecasting models miss the described effect, considering it rather a numerical artifact,” he adds. 

The researcher says that this laser-like effect of wave generation orthogonally to the wind can be observed not only in straits, but also in the open seas with specific inhomogeneous winds, where spatial wind turning points create conditions similar to those observed in presence of shores. 

The new research holds promise in explaining the nature of seiches, peculiar standing waves in semi-enclosed bodies of water that present a big problem for ships in ports. But it also suggests that a correct description of turbulence in the presence of coastlines will allow for rogue waves, seemingly unpredictable surface waves that are extremely dangerous even to large vessels.

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