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Register a new userThe excitation of rogue waves in a variable medium: an experimental study on the interaction of water waves and currents
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We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationaly unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped with a wavemaker and a pump for generating a current propagating in the opposite direction with respect to the waves. The experimental results support a recent conjecture based on a current-modified Nonlinear Schrodinger equation which establishes that rogue waves can be triggered by non-homogeneous current characterized by a negative horizontal velocity gradient.
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A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evidence is given that the rogue waves observed in the tank are hydrodynamic instantons, that is, saddle point configurations of the action associated with the stochastic model of the wave system. As shown here, these hydrodynamic instantons are complex spatio-temporal wave field configurations, which can be defined using the mathematical framework of Large Deviation Theory and calculated via tailored numerical methods. These results indicate that the instantons describe equally well rogue waves that originate from a simple linear superposition mechanism (in weakly nonlinear conditions) or from a nonlinear focusing one (in strongly nonlinear conditions), paving the way for the development of a unified explanation to rogue wave formation.
We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement techniques, whilst in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. Although significant progress in understanding rogue waves has been made based on an analogy between wave dynamics in optics and hydrodynamics, these comparisons have predominantly focused on one-dimensional nonlinear propagation scenarios. As a result, there remains significant debate about the dominant physical mechanisms driving the generation of ocean rogue waves in the complex environment of the open sea. Here, we review state-of-the-art of rogue wave studies in optics and hydrodynamics, aiming to clearly identify similarities and differences between the results obtained in the two fields. In hydrodynamics, we take care to review results that support both nonlinear and linear interpretations of ocean rogue wave formation, and in optics, we also summarise results from an emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems. We conclude with a discussion of important future research directions.
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonlinear theory based on the modal approach of (V. Shrira, A. Slunyaev, J. Fluid. Mech, 738, 65, 2014) leads to the one-dimensional modified nonlinear Schr{o}dinger equation of self-focusing type for a single mode. Its solutions such as envelope solitons and breathers are considered to be prototypes of rogue waves; these solutions, in contrast to waves in the absence of currents, are robust with respect to transverse perturbations, which suggests potentially higher probability of rogue waves. Robustness of the long-lived analytical solutions in form of the modulated trapped waves and solitary wave groups is verified by direct numerical simulations of potential Euler equations.
The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogue waves on the ocean caused by nonlinear focusing, is analyzed by direct numerical simulations based on two-phase Navier-Stokes equations. A finite-volume approach with a volume of fluid method is applied to study the Peregrine breather dynamics up to the initial stages of wave breaking. The comparison of the numerical results with laboratory experiments to validate the numerical approach shows very good agreement and suggests that the chosen method is an effective tool to study modulation instability and breather dynamics in water waves with high accuracy even up to the onset of wave breaking. The numerical results also indicate some previously unnoticed characteristics of the flow fields below the water surface of breathers, which might be of significance for short-term prediction of rogue waves. Recurrent wave breaking is also observed.
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom topography is taken into account since it also influences the local wave and current patterns. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types. The arising KdV equation with variable coefficients, dependent on the bottom topography, is studied numerically when the initial condition is in the form of the one soliton solution for the initial depth. Emergence of new solitons is observed as a result of the wave interaction with the uneven bottom.
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