分叉处水波的耦合条件
Coupling Conditions for Water Waves at Forks
摘要：
本文研究了非线性浅水波在呈分叉状的狭窄通道中的传播。我们的目的是计算耦合条件的一维有效模型，使用二维模拟和分析的基础上的守恒定律。对于小振幅，该分析证明了众所周知的Stoker界面条件，使得耦合不依赖于叉的角度。我们在数值解中也发现了这一点。由于对称性约束，对称分叉中的大振幅解也倾向于遵循Stoker关系。对于非对称分叉，2D效应占主导地位，因此有必要了解分叉内的流动。然而，即使这样，守恒定律也给了动力学一些启示。
英文摘要：
We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation laws. For small amplitudes, this analysis justifies the well-known Stoker interface conditions, so that the coupling does not depend on the angle of the fork. We also find this in the numerical solution. Large amplitude solutions in a symmetric fork also tend to follow Stoker's relations, due to the symmetry constraint. For non symmetric forks, 2D effects dominate so that it is necessary to understand the flow inside the fork. However, even then, conservation laws give some insight in the dynamics.
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