AI 中文总结
该研究推广Thorpe近似展开，分析切变流中海脊上潮汐产生的弱非线性内波，揭示离散谱模的非线性修正规律，解释线性模型与全非线性模拟吻合的原因。
AI 中文摘要
我们将Thorpe的逐次近似展开推广到Lamb和Dunphy提出的受迫、与潮汐锁定的内波生成问题，该问题中，正压潮汐流经海脊会在稳定切变流中辐射出离散谱的Taylor-Goldstein本征模。在地形陡度的二阶近似下，每个模通过闭式推导得到的对角模对核激发一个束缚二次谐波；对于均匀流，这两个核均消失，回归Thorpe极限。在三阶近似下，共振基模的可解性会产生非线性波数修正，这是Thorpe相速度偏移的受迫对应物，且潮汐频率固定。采用Lamb和Dunphy的参数进行计算表明，这些修正虽小但具有系统性：束缚谐波会适度扭曲位移剖面，且集中在下游模的表面切变层中；修正在第2至3模处达到峰值，随海脊高度和流强呈二次增长，且会使每个模发生非线性减速，从理论内部解释了为何线性离散谱模型能与完全非线性模拟吻合得如此之好。分层与切变层共置的密度跃层案例会大幅放大非线性修正，表明均匀分层的结论并非普适，且修正由N²相对于切变的位置控制。
英文摘要
We extend Thorpe successive approximation expansion to the forced, tide locked internal wave generation problem of Lamb and Dunphy, where a barotropic tide over a ridge radiates a discrete spectrum of Taylor Goldstein eigenmodes in a steady shear current. At second order in topographic steepness, each mode forces a bound second harmonic via diagonal mode pair kernels derived in closed form; both kernels vanish for uniform flow, recovering Thorpe limit. At third order, solvability of the resonant fundamental yields a nonlinear wavenumber correctionthe forced counterpart of Thorpe phase speed shift, with tidal frequency fixed. Computations at the parameters of Lamb and Dunphy show that the corrections are small but systematic, with the bound harmonic distorting the displacement profile modestly and concentrated in the surface shear layer for downstream modes. The corrections peak at modes 2 to 3, grow quadratically with ridge height and current strength, and amount to a nonlinear slow-down of every mode, explaining from within the theory why the linear discrete spectrum model agreed so well with fully nonlinear simulations. A pycnocline case with stratification colocated with the shear layer amplifies the nonlinear corrections substantially, showing that the uniform stratification verdict is not generic and that the corrections are controlled by where N2 sits relative to the shear.
Comments27 pages, 14 figures
