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Flying circus of physics

Extreme and rogue waves

Tuesday, April 01, 2014

Extreme and rogue waves
Jearl Walker
April 2014  Most ocean waves have heights within a certain range of values, which can be correlated with wind and storm conditions. However, larger waves sometimes occur.

If an extreme wave is described as having a frightening height, then a rogue wave would be described as having a terrifying height. It is preceded by a low point that is often characterized as a “hole in the water.” Large ships that were strong enough to withstand violent storms have been ripped apart as they slid bow downward into such a hole only to be wrenched upward by a wave standing some 30 meters above it. The height of the rogue wave that hit the U.S. Navy steamship Ramapo in 1933 was 34 meters, as measured by the officer on watch by triangulation of the crow’s nest against his view of the wave. (Doing physics in the face of death takes great physics courage.)

Both extreme and rogue waves have been spotted around the world, but the waters off the southeast coast of Africa produce more than their share of rogue waves, as verified by the many ships lost in the area. What causes extreme and rogue waves?

Here is the answer from the book The Flying Circus of Physics. For an ocean wave, you probably picture a sinusoidal wave (in the shape of a sine curve, with hills and valleys) moving over the ocean’s surface. If two waves traveling in the same direction were to overlap, you can imagine that the resultant wave (what you would see) is simply the addition of the two waves. If the waves were exactly aligned (in phase), the hills and valleys of the resultant wave would be higher and deeper than those on the individual waves. And if many waves, moving in different directions, overlapped, the resultant wave might be confusing to figure out, but simple addition of the individual waves should still give the height and depth of the resultant wave.

Such simple addition of waves is said to be a linear combination of the waves. Extreme waves seem to be a nonlinear combination; that is, the combination of individual waves somehow generates hills and valleys that are too high and too low. Perhaps as the hills grow, the wind over them enhances their growth so that the final hill height is greater than would be expected. Or perhaps in certain situations the buildup of a resultant wave past a critical point modifies the individual waves and creates an even larger resultant wave. In short, some feature enhances the resultant wave. The odds are against an extreme wave occurring, but occasionally such a wave slams into a cruise liner or some other ship, surprising captains who tend to think in terms of linear combinations.

Rogue waves (also called giant waves or freak waves) are even more difficult to explain but must also be due to a nonlinear combination of waves. However, their occurrence off the African southeast coast is surely due to the opposition of the Agulhas current and the wind-driven waves in the region. The strong Agulhas current flows toward the southwest in a meandering path; the wind-driven waves are typically toward the northeast. As the waves force the current to meander, they can be focused much like light waves can be focused by a lens. With the correct conditions, this focusing generates the hole in the water that is followed by a huge wave leaning toward the hole. Such a wave can kill, as reported in this next video:

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Journal reference style: author, journal, volume, pages (date)
Book reference style: author, title, publisher, date, pages
··· Shukla, P. K., I. Kourakis, B. Eliasson, M. Marklund, and L. Stenflo, “Instability and evolution of nonlinearly interacting water waves,” Physical Review Letters, 97, article # 094501 (1 September 2006)
··· Gibson, R. S., and C. Swan, “The evolution of large ocean waves: the role of local and rapid spectral changes,” Proceedings of the Royal Society A, 463, 21-48 (2007)
··· Kharif, C., J-P. Giovanangeli, J. Touboul, L. Grare, and E. Pelinovsky, “Influence of wind on extreme wave events: experimental and numerical approaches,” Journal of Fluid Mechanics, 594, 209-247 (2008)
· Garrett, C., and J. Gemmrich, “Rogue waves,” Physics Today, 62, No. 6, 62-63 (June 2009)
··· Rozhkov, S. S., “Giant freak waves: Expect the unexpected,” EPL (Europhysics Letters), 85, article # 24001 (6 pages) (2009)
··· Gronlund, A., B. Eliasson, and M. Marklund, “Evolution of rogue waves in interacting wave systems,” EPL (Europhysics Letters), 86, article # 24001 (5 pages) (2009)
··· Ruban, V. P., “Two different kinds of rogue waves in weakly crossing sea states,” Physical Review E, 79, article # 065304(R) (2009)
··· Chalikov, D., “Freak waves: Their occurrence and probability,” Physics of Fluids, 21, article # 076602 (18 pages) (2009)
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