The statistical treatment of random weakly nonlinear interactions between waves, called wave turbulence (WT), is fundamental to understanding the development of the ocean surface. For gravity waves, wave turbulence predicts a dual (direct and inverse) cascade of energy and wave action, which yield power-law solutions for the energy spectrum. While energy cascades were predicted more than 50 years ago, observing them in the laboratory with mechanical forcing remains a challenge. Here, we present experiments in which we attempted to reproduce both direct and inverse cascades in a large circular wave tank. The geometry of the wave tank allows for the creation of isotropically spread surface waves, which is an assumption that underlies WT theory. Although we did see evidence of a direct cascade of energy, we did not observe an inverse cascade of wave action. We discuss the competing effects of dissipation and intermittency, which may dominate or obscure the weakly nonlinear dynamics.

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the unidirectional nonlinear Schrödinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite; consequently, beam dynamics form. Spatiotemporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D + 1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large-amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose–Einstein condensates, solids, plasma, hydrodynamics, and optics.

Stationary wave groups exist in a range of nonlinear dispersive media, including optics, Bose-Einstein condensates, plasma, and hydrodynamics. We report experimental observations of nonlinear surface gravity X waves, i.e., X-shaped wave envelopes that propagate over long distances with constant form. These can be described by the 2D+1 nonlinear Schrödinger equation, which predicts a balance between dispersion and diffraction when the envelope (the arms of the X) travel at ±arctan(1/2)≈±35.26° to the carrier wave. Our findings may help improve understanding the lifetime of extremes in directional seas and motivate further studies in other nonlinear dispersive media.