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This article was submitted to Interdisciplinary Physics, a section of the journal Frontiers in Physics

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In this Brief Research Report, we show, within the framework of the nonlinear Schrödinger equation in deep water and in the presence of vorticity (vor-NLS), that the Peregrine breather traveling at the free surface of a shear current of slowly varying vorticity may transform into gray solitons.

Within the framework of a fully nonlinear two-dimensional potential solver [

We choose an Eulerian frame

In the case of a wave train propagating at the surface of a deep water flow of constant vorticity

[

Dimensionless group velocity deviation between finite and infinite depths as a function of the dispersive parameter for several values of the dimensionless vorticity. In dimensionless terms, the units of acceleration and length are the acceleration of gravity

The focusing vor-NLS equation admits the Peregrine breather as solution

Note that

Dimensionless profiles of the Peregrine breather

Within the framework of

The parameter σ is chosen such that the average temporal variation of the vorticity along the ramp is of

Time evolution of the tranformation of the Peregrine breather into a two-grey soliton with

Gray soliton profiles at

Within the framework of the vor-NLS equation in infinite depth we have shown numerically that a Peregrine breather propagating at the free surface of a slowly varying vortical flow may generate gray solitons. The present simulation confirms in a different context the result of [

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

HH, Conceptualization of the project, Methodology, and formal analysis checking. MA, Formal analysis checking; Software design; Numerical simulations; Validation; Investigation; Visualization. YC, Conceptualization of the project and formal analysis checking. CK, Conceptualization; Methodology; Formal analysis; Investigation; Writing.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.