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This chapter treats nonlinear wave-current interactions in their simplest form—as an overtaking collision. In one spatial dimension, the chapter investigates the collision interaction formulated as an initial value problem of a Burgers bore overtaking solutions of two types of nonlinear wave equations—Korteweg–de Vries (KdV) and nonlinear Schrödinger (NLS). The bore-wave state arising after the overtaking Burgers-KdV collision in numerical simulations is found to depend qualitatively on the balance between nonlinearity and dispersion in the KdV equation. The Burgers-KdV system is also made stochastic by following the stochastic advection by Lie transport approach (SALT).

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Collisions of Burgers Bores with Nonlinear Waves

  • 会议论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年

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  • Albert Dombret,
  • Darryl D. Holm,
  • Ruiao Hu,
  • Oliver D. Street,
  • Hanchun Wang

摘要

This chapter treats nonlinear wave-current interactions in their simplest form—as an overtaking collision. In one spatial dimension, the chapter investigates the collision interaction formulated as an initial value problem of a Burgers bore overtaking solutions of two types of nonlinear wave equations—Korteweg–de Vries (KdV) and nonlinear Schrödinger (NLS). The bore-wave state arising after the overtaking Burgers-KdV collision in numerical simulations is found to depend qualitatively on the balance between nonlinearity and dispersion in the KdV equation. The Burgers-KdV system is also made stochastic by following the stochastic advection by Lie transport approach (SALT).