论文标题
在平行剪切电流上长表面和内环波的波前和模态结构
Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current
论文作者
论文摘要
我们研究了在平行剪切流程中在分层流体中传播的长表面和内环波。环波的远场模态和振幅方程以维数表示。我们将它们从与环波切线的平面波的配方中重新介绍，这为获得环波的重要特征（例如组速度）开辟了一种方法，并构建了由环波的一部分和两个切线平面波组成的更通用的“混合溶液”。模态方程构成了一个新的光谱问题，并分析了在均匀流体和分层流体中均匀流体和内环波中表面环波的许多示例。针对具有线性剪切电流的两层流体的情况开发了详细的分析，我们研究了它们的波前和二维模态结构。进行比较是在均质和两层流体中表面波的模态函数以及准确和刚性近似中描述的界面波。我们还为幂律上层电流家族分析了表面和界面波的波前，可用于建模风流，河流流入和海峡中的流量。引入和评估了波前变形的全局和局部度量。
We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear flow. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive them from the formulation for plane waves tangent to the ring wave, which opens a way to obtaining important characteristics of the ring waves (e.g. group speed) and to constructing more general `hybrid solutions' consisting of a part of a ring wave and two tangent plane waves. The modal equations constitute a new spectral problem, and are analysed for a number of examples of surface ring waves in a homogeneous fluid and internal ring waves in a stratified fluid. The detailed analysis is developed for the case of a two-layered fluid with a linear shear current where we study their wavefronts and two-dimensional modal structure. Comparisons are made between the modal functions of the surface waves in a homogeneous and two-layered fluids, as well as the interfacial waves described exactly and in the rigid-lid approximation. We also analyse the wavefronts of surface and interfacial waves for a family of power-law upper-layer currents, which can be used to model wind generated currents, river inflows and exchange flows in straits. A global and local measure of the deformation of wavefronts are introduced and evaluated.
