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Mariners have long known of and feared the freak wave that can smash ocean-going vessels to smithereens. Understanding these rogue waves has been much more difficult.

One question is how they arise. The standard theories of wave scattering simply don’t allow rogue waves to form with anywhere near the frequency that anecdotal evidence would suggest.

Another problem is recreating the conditions that allow rogue waves to form in the lab so that any new thinking can be tested.

Now it looks as if oceanographers have a useful laboratory analogue with which to explore the freak wave phenomenon.

Eric Heller at Harvard University and various pals have studied rogue waves for some time. Today they show how microwaves propagating through a forest of scatterers which the team call a “quasi-two-dimensional resonator with randomly distributed scatterers, each mimicking an r^−2 repulsive potential”.

The results are fascinating because they clearly show the rogue waves (or hot spots in microwave terms) appearing more often than conventional thinking (Rayleigh’s law for the wave height distribution) allows. In fact the team says the probability in their set up of a rogue wave appearing is 15 orders of magnitude greater than Rayleigh statistics predict. They attribute the difference to ray refraction rather than to resonance effects as conventional thinking might suppose.

That kind of modeling might have useful implications for oceanographers hoping to study freak waves but also to astronomers who might like to better model the scattering that causes the twinkling of light from stars. Heller and co even suggest that rogue hot spots might be responsible for the lasing that occurs in random lasers.

Given that rogue waves seem to be more ubiquitous than anyone imagined, we’re likely to find them cropping up to explain all kinds of anomalous behaviour. They might even be worth exploiting if anyone can find a way to bend the nonlinear physics to their will.


Ref: arxiv.org/abs/0909.0847: Freak Waves in the Linear Regime: A Microwave Study

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