New hydroelastic solitary waves in deep water and their dynamics
New hydroelastic solitary waves in deep water and their dynamics
复制标题
DOI：
10.1017/jfm.2015.695
复制
发表时间：
2016-02-01
影响因子：
3.7
通讯作者：
Vanden-Broeck, J. -M.
中科院分区：
文献类型：
--
作者：
Gao, T.;Wang, Z.;Vanden-Broeck, J. -M.
本文研究了全非线性波在被柔性浮板覆盖的二维深层流体中的传播。bland （Arch）提出的非线性模型。老鼠。动力机械。分析的。， vol. 289, 2008, pp. 325-362)被用来表示薄弹性板施加的压力。Guyenne & Parau （J. fluid Meth, vol. 713, 2012, pp. 307-329）和Wang等人（IMA J. Appl.）先前发现的对称孤立波。数学，vol. 78, 2013, pp. 750-761)简要回顾。然后计算了波传播方向不对称的一类新的水弹性孤立波。这些不对称孤立波具有多包结构，并通过自发对称破缺分岔出现。我们详细地研究了纵向扰动下对称和非对称孤立波的稳定性。发现一些中等振幅对称孤立波是稳定的。通过一系列的数值实验，证明了两个稳定孤立波相互作用时的非弹性特性。局部稳定压力分布以略低于相速度最小值的速度移动（在文献中称为跨临界状态）所产生的大响应也进行了检查。对单载荷全非线性方程的直接数值模拟表明，在此范围内产生的波是有限振幅的。这包括一个受干扰的抑郁孤立波，它在性质上类似于在实验中观察到的大响应。稳定的高程孤立波的激励是通过施加在跨临界区以一定速度运动的多个载荷来实现的。
A numerical study of fully nonlinear waves propagating through a two-dimensional deep fluid covered by a floating flexible plate is presented. The nonlinear model proposed by bland (Arch. Rat. Mech. Anal., vol. 289, 2008, pp. 325-362) is used to formulate the pressure exerted by the thin elastic sheet. The symmetric solitary waves previously found by Guyenne & Parau (J. fluid Meth, vol. 713, 2012, pp. 307-329) and Wang et al. (IMA J. Appl. Maths, vol. 78, 2013, pp. 750-761) are briefly reviewed. A new class of hydroelastic solitary waves which are non-symmetric in the direction of wave propagation is then computed. These asymmetric solitary waves have a multi packet structure and appear via spontaneous symmetry-breaking bifurcations. We study in detail the stability properties of both symmetric and asymmetric solitary waves subject to longitudinal perturbations. Some moderate-amplitude symmetric solitary waves are found to be stable. A series of numerical experiments are performed to show the non-elastic behaviour of two interacting stable solitary waves. The large response generated by a localised steady pressure distribution moving at a speed slightly below the minimum of the phase speed (called the transcritical regime in the literature) is also examined. The direct numerical simulation of the fully nonlinear equations with a single load reveals that in this range the generated waves are of finite amplitude. This includes a perturbed depression solitary wave, which is qualitatively similar to the large response observed in experiments. The excitations of stable elevation solitary waves are achieved by applying multiple loads moving with a speed in the transcritical regime.