论文标题
对恒定涡度的深水上的孤立重力波的数值模拟
Numerical simulation of solitary gravity waves on deep water with constant vorticity
论文作者
论文摘要
我们介绍了一项数值研究，该研究是对深水在深水上的表面重力波的基本非线性动力学，并使用保形坐标中的处理方程持续涡度。已知表面重力波在剪切流上的分散关系具有两个分支，其中一个分支对于长波而言是弱分散的。该分支的波的弱非线性演变可以通过Benjamin-Ono方程来描述，该方程是可集成的，具有孤子和多索顿溶液。当前，在确切的Euler方程中保留了在弱非线性模型中获得的这种孤立波的性质的程度，尚不清楚。我们通过使用精确的Euler方程来研究这类孤立波的行为，而无需限制弱非线性的假设。对局部初始扰动的演变进行了建模，导致形成单孤波的形成，并讨论了有限振幅孤立波的特性。我们表明，在确切方程式的框架内，两索碰撞几乎是弹性的，但是与本杰明·诺克方程的溶液相反，波浪由于相互作用而获得相移。
We present a numerical study of essentially nonlinear dynamics of surface gravity waves on deep water with constant vorticity using governing equations in conformal coordinates. The dispersion relation of surface gravity waves on shear flow is known to have two branches, one of which is weakly dispersive for long waves. Weakly nonlinear evolution of the waves of this branch can be described by the Benjamin-Ono equation, which is integrable and has soliton and multi-soliton solutions. Currently, the extent to which the properties of such solitary waves obtained within the weakly nonlinear model are preserved in the exact Euler equations is unknown. We investigate the behaviour of this class of solitary waves without the restrictive assumption of weak nonlinearity by using the exact Euler equations. The evolution of localized initial perturbations leading to the formation of single or multiple solitary waves is modeled, and the properties of finite-amplitude solitary waves are discussed. We show that within the framework of the exact equations, two-soliton collisions are almost elastic, but in contrast to solutions of the Benjamin-Ono equation the waves receive a phase shift as a result of the interaction.
