Spectral up- and downshifting of Akhmediev breathers under wind forcing

TL;DR

This study combines experiments and numerical modeling to analyze how wind forcing affects the spectral dynamics of Akhmediev breathers, revealing mechanisms for spectral up- and downshifting influenced by wind and dissipation.

Contribution

The paper develops a higher-order wind model aligned with the Dysthe equation, providing new insights into spectral shifts of Akhmediev breathers under wind forcing.

Findings

Leading order wind forcing broadens the spectrum.

Higher order asymmetric wind term causes spectral upshift.

Dissipative effects can induce spectral downshift.

Abstract

We experimentally and numerically investigate the effect of wind forcing on the spectral dynamics of Akhmediev breathers, a wave-type known to model the modulation instability. We develop the wind model to the same order in steepness as the higher order modifcation of the nonlinear Schroedinger equation, also referred to as the Dysthe equation. This results in an asymmetric wind term in the higher order, in addition to the leading order wind forcing term. The derived model is in good agreement with laboratory experiments within the range of the facility's length. We show that the leading order forcing term amplifies all frequencies equally and therefore induces only a broadening of the spectrum while the asymmetric higher order term in the model enhances higher frequencies more than lower ones. Thus, the latter term induces a permanent upshift of the spectral mean. On the other hand, in contrast to the direct effect of wind forcing, wind can indirectly lead to frequency downshifts, due to dissipative effects such as wave breaking, or through amplification of the intrinsic spectral asymmetry of the Dysthe equation. Furthermore, the definitions of the up- and downshift in terms of peak- and mean frequencies, that are critical to relate our work to previous results, are highlighted and discussed.