波浪破碎引起的爆炸波纹不稳定性
Explosive ripple instability due to incipient wave breaking
摘要：
考虑具有自由表面和有限深度的二维理想势流，研究了在变陡非线性波背景下小振幅短波长波列的动力学行为。这可以看作是碎波带中碎波斜坡上小波纹发展的模型。利用波作用量作为绝热不变量的概念，我们导出了波纹陡度变化的显式渐近表达式。通过这个表达式，非线性效应被描述为使用固有频率和固有重力沿拉格朗日（材料）轨迹上的自由表面。我们表明，强大的压缩附近的尖端波导致爆炸性（超指数）波纹不稳定。这种不稳定性对于理解破碎波表面的破碎和白浪现象具有重要意义。分析结果证实了使用潜在的理论模型的数值模拟。
英文摘要：
Considering two-dimensional potential ideal flow with free surface and finite depth, we study the dynamics of small-amplitude and short-wavelength wavetrains propagating on the background of a steepening nonlinear wave. This can be seen as a model for small ripples developing on slopes of breaking waves in the surf zone. Using the concept of wave action as an adiabatic invariant, we derive an explicit asymptotic expression for the change of ripple steepness. Through this expression, nonlinear effects are described using the intrinsic frequency and intrinsic gravity along Lagrangian (material) trajectories on a free surface. We show that strong compression near the tip on the wave leads to an explosive (super-exponential) ripple instability. This instability may play important role for understanding fragmentation and whitecapping at the surface of breaking waves. Analytical results are confirmed by numerical simulations using a potential theory model.
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