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<p>Under the shallow-water regime and without assuming wave amplitude smallness, we apply the variational approach in the Lagrangian formalism to derive the geophysical Green-Naghdi system. In contrast to the prior derivation in (Fan et al., J. Nonlinear Sci., <b>32</b>(21), 30 (2022)) that imposed a columnar-flow Ansatz, our method adopts the irrotational-flow assumption (which Fan et al., J. Nonlinear Sci., <b>32</b>(21), 30 (2022) does not), thereby generating the depth-independent horizontal velocity at leading order.</p>

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Variational Derivation of the Geophysical Green-Naghdi Shallow-water System

  • 期刊论文

  • 发表日期：

    2025年9月11日

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  • Yue Chen,
  • Xingxing Liu

摘要

Under the shallow-water regime and without assuming wave amplitude smallness, we apply the variational approach in the Lagrangian formalism to derive the geophysical Green-Naghdi system. In contrast to the prior derivation in (Fan et al., J. Nonlinear Sci., 32(21), 30 (2022)) that imposed a columnar-flow Ansatz, our method adopts the irrotational-flow assumption (which Fan et al., J. Nonlinear Sci., 32(21), 30 (2022) does not), thereby generating the depth-independent horizontal velocity at leading order.