2024/09/28 by Marcelo V. Flamarion, Efim Pelinovsky, Flamarion, Marcelo V. +1 · 1 citation
Earth and Planetary Sciences · Mathematics · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Ocean Waves and Remote Sensing #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2409.19424
openalex publication_date 2024/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we study the evolution of disturbances within the framework of the Cubic Vortical Whitham (CV-Whitham) equation, considering both positive and negative cubic nonlinearities. This equation plays important role for description of the wave processes in the presence of shear flows. We find well-formed breather-type structures arising from the evolution of depression disturbances with positive cubic nonlinearity. For elevation disturbances, the results are two-fold. When the cubic nonlinearity is negative, we show that the CV-Whitham equation and the Gardner equation are qualitatively similar, differing only by a small phase lag due to differences in the dispersion term. However, with positive cubic nonlinearity, the differences between the solutions become more pronounced, with the CV-Whitham equation producing sharper waves that suggest the onset of wave breaking.