A conformal-mapping technique for topographic-wave problems: semi-infinite channels and elongated basins
A conformal-mapping technique for topographic-wave problems: semi-infinite channels and elongated basins
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地形波问题的共形映射技术：半无限通道和细长盆地
DOI：
10.1017/s0022112087001010
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发表时间：
1987
影响因子：
3.7
通讯作者：
E. Johnson
中科院分区：
文献类型：
--
作者：
E. Johnson
通过考虑Davis（1983）指出的线性正压势涡方程在共形映射下的不变性，更详细地讨论了Johnson（1985）的地形波问题的共形映射方法的基础。提出了一种利用这一性质来构造在不同地形上传播的波的进一步解的方法。给出了半无限通道和拉长盆地的结果。构造了一个随端壁距离以指数速度逼近直角坐标系的坐标系。对于指数级倾斜地形，无限通道、半无限通道和盆地的解具有与椭圆盆地中的波相同的结构和色散关系，Johnson（1987）对此进行了讨论。因此，在某种意义上，所提出的结构可以被认为是指数倾斜地形的通用结构。
The basis of the conformal-mapping method for topographic-wave problems of Johnson (1985) is discussed in greater detail by considering the invariance under conformal mapping of the linear, barotropic, potential-vorticity equation, noted in Davis (1983). A method is presented for using this property to construct further solutions for waves propagating over varying topography. Results are given for semi-infinite channels and elongated basins. A coordinate system is constructed that approaches a Cartesian system exponentially fast with distance from end-walls. For exponentially sloping topography the solutions for infinite channels, semi-infinite channels, and basins have the same structure and dispersion relation as waves in an elliptical basin, discussed in Johnson (1987). The structures presented there can thus be considered as in some sense universal for exponentially sloping topography.