Solitary and periodic gravity—capillary waves of finite amplitude
Solitary and periodic gravity—capillary waves of finite amplitude
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DOI：
10.1017/s0022112083003316
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发表时间：
1983-09
影响因子：
3.7
通讯作者：
J. K. Hunter;J. Vanden-Broeck
中科院分区：
文献类型：
--
作者：
J. K. Hunter;J. Vanden-Broeck
本文研究了有限水深中的二维孤立波和周期波。波在重力和表面张力的共同影响下传播。流动、表面轮廓和相速度是波的振幅和参数l = λ/H和τ = T/ρ gH 2的函数。这里λ是波长，H是深度，T是表面张力，ρ是密度，g是重力加速度。当$\dot{\tau} >\frac{1}{3}$，l值较大，振幅值较小时，波的剖面近似满足Korteweg-de弗里斯方程。然而，当τ接近$\frac{1}{3}$时，这个等式就失效了。本文给出了τ接近1/3时的一个新方程。此外，一个数值方案的基础上的积分微分方程制定，推导出解决问题的完全非线性的情况下。给出了周期波和孤立波的精确解。数值结果表明，当$\tau < \frac{1}{3}$时，Korteweg-de弗里斯方程不能准确描述周期性重力-毛细波。此外，当波长趋于无穷大时，无法获得作为周期波连续极限的高程孤立波。结果的图表包括在内。
Two-dimensional solitary and periodic waves in water of finite depth are considered. The waves propagate under the combined influence of gravity and surface tension. The flow, the surface profile and the phase velocity are functions of the amplitude of the wave and the parameters l = λ/H and τ = T/ρgH2. Here λ is the wavelength, H the depth, T the surface tension, ρ the density and g the acceleration due to gravity. For $\dot{\tau} >\frac{1}{3}$, large values of l and small values of the amplitude, the profile of the wave satisfies the Korteweg–de Vries equation approximately. However, for τ close to $\frac{1}{3}$ this equation becomes invalid. In the present paper a new equation valid for τ close to 1/3 is obtained. Moreover, a numerical scheme based on an integrodifferential-equation formulation is derived to solve the problem in the fully nonlinear case. Accurate solutions for periodic and solitary waves are presented. The numerical results show that the Korteweg–de Vries equation does not provide an accurate description of periodic gravity-capillary waves for $\tau < \frac{1}{3}$. In addition, it is shown that elevation solitary waves cannot be obtained as the continuous limit of periodic waves as the wavelength tends to infinity. Graphs of the results are included.