AI 中文总结
研究风暴潮中普劳德曼共振问题，通过给出非线性精确解，一阶近似类似原解，二阶近似得有限解，表明非线性可抑制共振。此解对低压系统普遍适用，对高压系统有局限，F越近1越易失效，还指出原解在不同条件下的准确性差异。
AI 中文摘要
风暴和恶劣天气常与大气低压系统相关。移动的低压系统产生的风暴潮取决于波浪弗劳德数（F）。普劳德曼对此问题的共振在F = 1时趋于无穷。本文通过给出非线性精确解重新审视该问题，一阶近似回到普劳德曼解，二阶近似给出包括共振处的有限解，表明非线性平流可显著抑制共振。共振时解虽有限但 bifurcates 成两个分支，与理论流体动力学和许多非线性系统中的混沌有关。普劳德曼解对所有低压系统都存在，但对移动高压系统引起的强迫波仅在有限范围内有效，F越接近1，高压系统的解越易失效。研究还发现普劳德曼解仅在亚临界条件下最准确，超临界条件下误差大得多。
英文摘要
Storms and severe weather are often associated with atmospheric low-pressure systems. A moving low atmospheric pressure system produces storm surge that is dependent on the wave Froude number (F) or the ratio between the speed of the storm and the shallow water wave propagation speed. Proudman's resonance for such a problem goes to infinity at F=1. This work revisits the problem by presenting a nonlinear exact solution. The first order approximation goes back to Proudman's solution. The second order approximation provides a finite solution including at resonance. The solution shows that the nonlinear advection can significantly suppress the resonance. At resonance, although the solution is finite, it bifurcates into two branches, a condition linked to chaos in theoretical fluid dynamics and many nonlinear systems. Although Proudman's solution does not provide any limit to the atmospheric pressure system, it is not without any condition. The solution exists for all low-pressure systems but has only limited validity for a moving atmospheric high-pressure system induced forced waves: at low moving speed, the solution under a high-pressure system can exist for a range of high-pressure variability but quickly become invalid as the system's speed increases. The closer F is to 1 (resonance), the easier for the solution to be invalidated for a high-pressure system. This study also found that Proudman's solution is most accurate only under subcritical conditions with small low-pressure variability and has much larger error under supercritical conditions.
Comments19 pages and 4 figures
Journal refLi, C. (2025). Nonlinear Proudman Resonance Under Moving Atmospheric System. Journal of Nonlinear Mathematical Physics, 32:97
DOI：10.1007/s44198-025-00345-x.
