A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia-gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hami...

Rogue waves is the name given by oceanographers to isolated large amplitude waves, that occur more frequently than expected for normal, Gaussian distributed, statistical events. Rogue waves are ubiquitous in nature and appear in a variety of different contexts. Besides water waves, they have been recently reported in liquid Helium, in nonlinear optics, microwave cavities, etc. The first part of...

s : Regularization through stochastic forcing and its impact on nonlinear time-reversal A. Nachbin IMPA, Est. D. Castorina, 110, J. Botanico, CEP 22460-320, Rio, RJ, Brasil A large amount of mathematical theory has been developed for the time-reversal of linear waves in random media. This work concerns the extension to one-dimensional, weakly nonlinear water waves. Weakly dispersive water waves...

Periodic progressive waves in shallow to transitional water are described by a Cnoidal Approximation wave theory. The formulation is analytical and largely classical. Periodic waves are assumed, so that the theory does not extend to solitary waves. The solution is completed numerically, as a problem in nonlinear optimisation. The suitability of the theory in shallow to transitional water is dem...

[1] We report on near-bottom waves of elevation with amplitude nearly half the 25 m water column, very steep, and propagating into a sheared turbulent waveguide. The waves contained trapped cores transporting parcels of water shoreward. These large waves depart strongly from weakly-nonlinear and weakly-nonhydrostatic conditions and challenge established paradigms. They can also represent an imp...