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<p>In this paper, we study the existence of large-amplitude two-dimensional periodic stratified gravity waves that propagate along the free surface of a water flow over a flat bed. Both the Bernoulli function and the density gradient admit to be arbitrarily discontinuous. The discontinuities in the Bernoulli function and the density gradient require new analytical techniques to prove our main results. Within the weak formulation framework, we examine laminar flow solutions and characterize bifurcation points via an integral equation, thereby obtaining the corresponding global bifurcation results.</p>

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Large-amplitude stratified gravity water waves with discontinuous density gradient

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Zihao Wang,
  • Yong Zhang

摘要

In this paper, we study the existence of large-amplitude two-dimensional periodic stratified gravity waves that propagate along the free surface of a water flow over a flat bed. Both the Bernoulli function and the density gradient admit to be arbitrarily discontinuous. The discontinuities in the Bernoulli function and the density gradient require new analytical techniques to prove our main results. Within the weak formulation framework, we examine laminar flow solutions and characterize bifurcation points via an integral equation, thereby obtaining the corresponding global bifurcation results.