Waves on currents, including connections with rogue waves

waves-on-currents The interaction between waves and currents continues to be a major challenge in the theory of water waves.  In his opening lecture Victor Shrira will be speaking on trapped waves on jet currents.  An asymptotic theory of surface waves trapped on vertically uniform jet currents has been recently developed as a first step towards a systematic description of wave dynamics on oceanic jet currents.  It has been shown that in a linear setting an asymptotic separation of vertical and horizontal variables, which underpins the modal description of the wave field on currents, is possible if either the current velocity is small compared to the wave celerity or the current width is large compared to the wavelength along the current.  Asymptotic solutions are developed and they proved not only to capture qualitative behaviour well but also to provide a good quantitative description even for unrealistically strong and narrow currents. The results are discussed for various oceanic currents, with particular attention paid to the Agulhas Current, for which specific estimates were derived.  The theory also leads to the one-dimensional modified nonlinear Schrödinger 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 a potentially higher probability of rogue waves. Some of this work has appeared in the papers Trapped waves on jet currents: asymptotic modal approach,  published in the J Fluid Mechanics, and  Nonlinear dynamics of trapped waves on jets, published in Physical Review E, both by V.I. Shrira & A.V. Slunyaev.

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