X-Waves and Modulation Instability

Abstract

Modulation instability is characterised by a rapid transfer of energy from a dominant central frequency to sideband frequencies. Dispersive media such as water, optics, and Bose-Einstein condensate, all allow for modulation instability. In the space-time domain, modulation instability manifests itself as a single extreme wave crest arising from an initially periodic, constant amplitude wavetrain. Given the sudden appearance of an unexpectedly high wave crest, the modulation instability has long been proposed as a mechanism by which extreme ocean waves are formed. In this talk I will present the experimental work performed with various collaborators in both the University of Edinburgh’s circular basin (FloWave) and University College London’s combined wave-current flume. In the FloWave basin we observed the propagation of a nondispersive X-wave,a wave structure capable of transporting an extremely large wave at its centre over vast distances without dispersing. The X-wave was predicted using the three-dimensional nonlinear Schrödinger equation (NLSE) to balance nonlinear, dispersive, and diffractive wave properties. At University College London we showed experimentally how a linear vertically sheared current reduces the growth rate of modulation instability as predicted by a modified version of the NLSE, the constant vorticity NLSE (vor-NLSE).At University College London we showed experimentally how a linear vertically sheared current reduces the growth rate of modulation instability as predicted by a modified version of the NLSE, the constant vorticity NLSE (vor-NLSE).At University College London we showed experimentally how a linear vertically sheared current reduces the growth rate of modulation instability as predicted by a modified version of the NLSE, the constant vorticity NLSE (vor-NLSE).