Vortices near barriers with multiple gaps
Vortices near barriers with multiple gaps
复制标题
具有多个间隙的障碍物附近的涡流
DOI：
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发表时间：
2005
影响因子：
3.7
通讯作者：
N. R. McDonald
中科院分区：
文献类型：
--
作者：
E. Johnson;N. R. McDonald
提出了两个模型来描述无限长障碍物间隙附近的涡流运动。第一个模型考虑线涡旋，通过分析获得满足控制二维欧拉方程的精确非线性轨迹。第二个模型考虑恒定涡度的有限区域斑块，并基于共形映射和轮廓手术的数值方法。这两个模型可以比较线涡和涡斑的轨迹。详细考虑了位于两个岬角之间的岛屿形成的双缺口的情况。值得注意的是，开尔文定理将岛屿周围的环流限制为常数，从而迫使岛屿和岬角之间的体积通量随时间变化。当岛屿和岬角之间的间隙很小时，该通量需要任意大的流速通过间隙。在大多数示例中，斑块的质心被限制为紧密遵循同一循环的线涡旋的轨迹。当穿过间隙的流动迫使涡流斑块靠近岛的边缘时，会发生例外，涡流在岛的边缘处分裂成两部分，并且只有部分涡流穿过间隙。一般来说，挤压通过狭窄间隙的零件会恢复到接近圆形，其直径明显大于间隙宽度。
Two models are presented for the motion of vortices near gaps in infinitely long barriers. The first model considers a line vortex for which the exact nonlinear trajectories satisfying the governing two-dimensional Euler equations are obtained analytically. The second model considers a finite-area patch of constant vorticity and is based on conformal mapping and the numerical method of contour surgery. The two models enable a comparison of the trajectories of line vortices and vortex patches. The case of a double gap formed by an island lying between two headlands is considered in detail. It is noted that Kelvin's theorem constrains the circulation around the island to be a constant and thus forces a time-dependent volume flux between the islands and the headlands. When the gap between the island and a headland is small this flux requires arbitrarily large flow speeds through the gap. In most examples the centroid of the patch is constrained to follow closely the trajectory of a line vortex of the same circulation. Exceptions occur when the through-gap flow forces the vortex patch close to an edge of the island where it splits into two with only part of the vortex passing through the gap. In general the part squeezing through a narrow gap returns to near-circular to have a diameter significantly larger than the gap width.