耦合表面和internal waves在有流情况下的哈密顿模型
Hamiltonian model for coupled surface and internal waves in the presence of currents
摘要：
我们研究了一个二维流体系统，该系统由一个由平板和一个具有自由表面的上层介质组成的下层介质组成。这两种媒体由一个免费的公共接口分开。在一定的物理假设下，重力驱动的表面和内部水波（在介质之间的共同界面）的存在下的深度依赖的电流进行了研究。这两种介质都被认为是不可压缩的，并具有规定的涡流。利用哈密顿方法，构造了系统的哈密顿量的“波”变量和运动方程的计算。由此产生的运动方程，然后分析表明，波流相互作用的影响，只有在“带”相邻的表面和界面的电流剖面。还提出了小振幅和长波近似。
英文摘要：
We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of 'wave' variables and the equations of motion are calculated. The resultant equations of motion are then analysed to show that wave-current interaction is influenced only by the current profile in the 'strips' adjacent to the surface and the interface. Small amplitude and long-wave approximations are also presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
