Elliptica topographic waves
Elliptica topographic waves
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椭圆形地形波
DOI：
10.1080/03091928508219266
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发表时间：
1985
影响因子：
1.3
通讯作者：
L. Mysak
中科院分区：
文献类型：
--
作者：
L. Mysak
摘要 提出了某种类型椭圆盆地中非发散地形波（旋转模态）的简单解析解。假设盆地的深度等值线形成一系列共焦椭圆，椭圆柱坐标中的控制位涡方程可简化为笛卡尔形式，与坐标尺度因子无关。因此，对于指数深度剖面 h=e −bψ，其中 xi 是径向坐标，沿中心线具有部分垂直屏障的盆地中椭圆行波的径向特征函数可以用初等函数表示。对于没有障碍物的湖泊，通过Rayleigh-Ritz（变分）方法获得近似解析解。变分解的前几个模式的周期和流线模式与 Ball (1965) 的椭圆抛物面的周期和流线模式进行了比较。还计算了变分解之一的最严重模式周期......
Abstract Simple analytical solutions are presented for nondivergent topographic waves (rotational modes) in a certain type of elliptical basin. Under the assumption that the basin's depth contours form a family of confocal ellipses, the governing potential vorticity equation in elliptic cylindrical coordinates reduces to a Cartesian form, independent of the coordinate scale factors. As a consequence, for the exponential depth profile h=e −bξ, where ξ is the radial coordinate, the radial eigenfunctions for elliptically travelling waves in a basin with a partial vertical barrier along the centerline can be expressed in terms of elementary functions. For a lake without a barrier, approximate analytical solutions are obtained by the Rayleigh-Ritz (variational) method. The periods and streamline patterns of the first few modes of the variational solutions are compared with those due to Ball (1965) for an elliptic paraboloid. The gravest mode period of one of the variational solutions has also been computed for...