Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances
Experiments and analyses of upstream-advancing solitary waves generated by moving disturbances
复制标题
DOI：
10.1017/s0022112089000492
复制
发表时间：
1989-02
影响因子：
3.7
通讯作者：
Seung-Joon Lee;G. T. Yates;T. Y. Wu
中科院分区：
文献类型：
--
作者：
Seung-Joon Lee;G. T. Yates;T. Y. Wu
在这个联合的理论，数值和实验研究中，我们调查的非线性波的强迫产生的扰动稳定地通过一层浅水跨临界速度移动的现象。这里考虑的平面运动是由广义Boussinesq方程和强迫Korteweg-de弗里斯（fKdV）方程，这两个承认两种类型的强迫机构的形式的外部表面压力和底部地形。数值结果得到使用两种理论模型的两种类型的强迫。这些结果表明，在跨临界速度范围内，一系列孤立波的产生，周期性和无限的，形成一个游行前进上游的扰动，而一列弱非线性和弱色散波的下游发展的一个不断延长的拉伸的均匀凹陷的水面后面的干扰。这是一个很好的例子，说明了动力系统对定常强迫的响应不需要渐近地趋向于定常状态，但在脉冲启动后，当系统被迫共振时，它可以是明显的周期性的。一系列实验室实验是在一个弧形的海底地形上进行的，从静止到恒定的跨临界速度U，相应的深度弗劳德数F = U/（gh 0）½（g是重力常数，h 0是原始的均匀水深）几乎是一个临界值。对于这两种类型的强迫，广义Boussinesq模型表明，表面压力可以更有效地产生前孤立波比淹没地形相同的归一化空间分布。然而，根据fKdV模型，这两种类型的强迫是完全等效的。除了这些和其他一些相当精细的差异之外，在理论和实验之间发现了广泛的一致性，无论是在所产生的波的振幅和相位方面，当速度接近临界时（0.9 F > 0.2，最终在F> 0.2时消失）。在另一个方向上，当弗劳德数增加到F <$1.2以上时，发现前体孤立子现象也会消失，因为没有有限振幅孤立波可以超越快速移动的扰动，也没有任何二维波可以继续跟随。在这个超临界范围内，对于渐近大的时间，所有的影响仍然只是局部的干扰。从而确定了产生前兆孤子这一奇妙现象的判据。
In this joint theoretical, numerical and experimental study, we investigate the phenomenon of forced generation of nonlinear waves by disturbances moving steadily with a transcritical velocity through a layer of shallow water. The plane motion considered here is modelled by the generalized Boussinesq equations and the forced Korteweg-de Vries (fKdV) equation, both of which admit two types of forcing agencies in the form of an external surface pressure and a bottom topography. Numerical results are obtained using both theoretical models for the two types of forcings. These results illustrate that within a transcritical speed range, a succession of solitary waves are generated, periodically and indefinitely, to form a procession advancing upstream of the disturbance, while a train of weakly nonlinear and weakly dispersive waves develops downstream of an ever elongating stretch of a uniformly depressed water surface immediately behind the disturbance. This is a beautiful example showing that the response of a dynamic system to steady forcing need not asymptotically tend to a steady state, but can be conspicuously periodic, after an impulsive start, when the system is being forced at resonance. A series of laboratory experiments was conducted with a cambered bottom topography impulsively started from rest to a constant transcritical velocity U, the corresponding depth Froude number F = U/(gh0)½ (g being the gravitational constant and h0 the original uniform water depth) being nearly the critical value of unity. For the two types of forcing, the generalized Boussinesq model indicates that the surface pressure can be more effective in generating the precursor solitary waves than the submerged topography of the same normalized spatial distribution. However, according to the fKdV model, these two types of forcing are entirely equivalent. Besides these and some other rather refined differences, a broad agreement is found between theory and experiment, both in respect of the amplitudes and phases of the waves generated, when the speed is nearly critical (0.9 F > 0.2, finally disappear at F ≈ 0.2. In the other direction, as the Froude number is increased beyond F ≈ 1.2, the precursor soliton phenomenon was found also to evanesce as no finite-amplitude solitary waves can outrun, nor can any two-dimensional waves continue to follow, the rapidly moving disturbance. In this supercritical range and for asymptotically large times, all the effects remain only local to the disturbance. Thus, the criterion of the fascinating phenomenon of the generation of precursor solitons is ascertained.