Interacting solitary waves

Interacting solitary waves. Ever since John Scott Russell first reported a large, long-lived, solitary wave of constant shape on a Scottish canal in 1834, such waves have been an active area of research in diverse fields that include not only oceanography but also optics, cosmology, plasma physics, and even biophysics. Dubbed solitons, solitary waves are inherently nonlinear, and their velocities depend on amplitude. When two collide in one dimension, they can appear to bounce off each other or to have the faster one jump over the slower one. In 2D, even more complex interactions can occur. Mark Ablowitz and Douglas Baldwin of the University of Colorado Boulder report observing surprisingly frequent, varied nonlinear interactions between multiple solitary water waves at two flat beaches; the photo is an example of the aptly named “Y-type” interaction. (Additional photos and videos of Y-type and other interactions are available at the hyperlinks above.) The two mathematicians found that the interactions usually occur, albeit briefly, at shallow depths within two hours of low tide; tend to come in groups; and are remarkably robust against changes in depth, wind perturbations, and even breaking. The diverse wave structures are well modeled using a 2D nonlinear wave equation. The same equation, note the researchers, approximates the propagation of tsunamis, and the pair warns that similar nonlinear interactions could significantly amplify a tsunami’s destructive power. (M. J. Ablowitz, D. E. Baldwin, Phys. Rev. E 86, 036305, 2012.)