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<p>This study focuses on the wave-breaking phenomenon in geophysical water flows exhibiting azimuthal propagation and discontinuous, piecewise constant stratification. Wave-breaking—understood as the scenario in which the wave remains bounded up to the maximal existence time, at which point its slope becomes infinite—is one of the most prominent types of singularities encountered in the analysis of nonlinear partial differential equations. A notable outcome of our analysis is that, while the surface wave breaks in finite time, the internal interface—arising from the density discontinuity between the bottom and near-surface layers—persists for all time. This behaviour aligns closely with observations in real-world geophysical settings.</p>

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Free surface wave-breaking in the full nonlinear water wave problem with a permanent interface in cylindrical coordinates

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Calin I. Martin

摘要

This study focuses on the wave-breaking phenomenon in geophysical water flows exhibiting azimuthal propagation and discontinuous, piecewise constant stratification. Wave-breaking—understood as the scenario in which the wave remains bounded up to the maximal existence time, at which point its slope becomes infinite—is one of the most prominent types of singularities encountered in the analysis of nonlinear partial differential equations. A notable outcome of our analysis is that, while the surface wave breaks in finite time, the internal interface—arising from the density discontinuity between the bottom and near-surface layers—persists for all time. This behaviour aligns closely with observations in real-world geophysical settings.