High-order strongly nonlinear long wave approximation and solitary wave solution. Part 2. Internal waves
High-order strongly nonlinear long wave approximation and solitary wave solution. Part 2. Internal waves
复制标题
DOI：
10.1017/jfm.2022.950
复制
发表时间：
2022-12
影响因子：
3.7
通讯作者：
W. Choi
中科院分区：
文献类型：
--
作者：
W. Choi
采用强非线性长波近似，假定水深远小于典型波长，得到了两层系统中大振幅长内波的高阶模型。当一阶截断时，该模型可归结为Choi等人的正则化强非线性模型。(《流体力学》，2009年，第629卷，第73-85页)，它减少了无粘性Miyata-Choi-Camassa(MCC)方程中由界面切向速度跳跃引起的Kelvin-Helmholtz不稳定性。利用二阶模型对MCC方程的内孤立波解进行了二阶修正，并用欧拉解从波型、有效波长和速度分布三个方面对其有效性进行了检验。结果表明，在整个波幅范围内，修正后的结果与欧拉解相比有了很大的改善，实际应用中不需要进一步修正。在局部稳定性分析的基础上，在物理参数空间中确定了二阶长波模式的稳定区域，从而使为一阶模式开发的高效数值格式可以应用于二阶模式。
Abstract A strongly nonlinear long-wave approximation is adopted to obtain a high-order model for large-amplitude long internal waves in a two-layer system by assuming the water depth is much smaller than the typical wavelength. When truncated at the first order, the model can be reduced to the regularized strongly nonlinear model of Choi et al. (J. Fluid Mech., vol. 629, 2009, pp. 73–85), which lessens the Kelvin–Helmholtz instability excited by the tangential velocity jump across the interface in the inviscid Miyata–Choi–Camassa (MCC) equations. Using the second-order model, the next-order correction to the internal solitary wave solution of the MCC equations is found and its validity is examined with the Euler solution in terms of the wave profile, the effective wavelength and the velocity profile. It is shown that the correction greatly improves the comparison with the Euler solution for the whole range of wave amplitudes and no further correction is necessary for practical applications. Based on a local stability analysis, the region of stability for the second-order long-wave model is identified in the physical parameter space so that the efficient numerical scheme developed for the first-order model can be used for the second-order model.