Synopsis

Alphabet Waves

Physics 5, s136
Researchers explain where those X- and Y-shaped waves at the shore come from.
M. J. Ablowitz and D. E. Baldwin, Phys. Rev. Lett. (2012)

While many beachcombers head home with nothing but a few seashells and a sunburn, two scientists have made productive use of their time in the waves. At two beaches on the Pacific coast of California and Mexico, they discovered that nonlinear wave patterns, in particular X- and Y-shaped waves, are surprisingly common. As reported in Physical Review E by Mark Ablowitz and Douglas Baldwin of the University of Colorado, Boulder, these wave phenomena may contribute to the growth of tsunami waves.

Water waves are difficult to model mathematically, since the underlying equations are strongly nonlinear. Under certain conditions, these nonlinear effects can produce solitary waves called solitons that travel long distances without losing their shape. Most solitons propagate along a single-line wave front, but if two waves merge at an angle, complicated two-dimensional patterns can form. These nonlinear interactions can create wave heights that are higher than the sum of the individual waves, which may amplify the destructive power of tsunamis.

Previously, the assumption was that these interactions are rare. However, the authors have observed thousands of X and Y waves shortly before and after low tide at two flat beaches, where water depths were less than about 20 centimeters. The researchers showed that the shallow waves recorded in their photographs and films (see examples of the authors’ videos and photos) could be accurately described by a two-dimensional nonlinear wave equation. – Michael Schirber


Subject Areas

Nonlinear DynamicsFluid Dynamics

Related Articles

Ultrafast, Self-Propelled Particles
Soft Matter

Ultrafast, Self-Propelled Particles

New “Marangoni surfers” that whizz along at 10,000 body lengths per second offer new insight into active matter propelled by surface-tension gradients. Read More »

Small Spheres Freeze When Hot
Fluid Dynamics

Small Spheres Freeze When Hot

An optofluidic effect causes a group of fluid-suspended particles to “freeze” when one of them is heated, potentially allowing greater control over these systems. Read More »

Active Matter that Mimics Turbulence in Space and Time
Soft Matter

Active Matter that Mimics Turbulence in Space and Time

Despite being driven by a different process, a system of self-propelling particles can evolve over time in a similar way to a turbulent fluid. Read More »

More Articles