A family of helically symmetric vortex equilibria
A family of helically symmetric vortex equilibria
复制标题
一族螺旋对称涡旋平衡
DOI：
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发表时间：
2009
影响因子：
3.7
通讯作者：
D. Dritschel
中科院分区：
文献类型：
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作者：
D. Lucas;D. Dritschel
在不可压缩的无粘无旋无限流体中，我们提出了一族由螺旋对称涡旋组成的稳定旋转平衡态。这些涡旋由均匀轴向涡度的等高线边界区域来描述。当平行于涡线的流场与(1+ϵ2R2)−1/2成正比时，螺旋对称性意味着(在绝对参照系中)轴向涡量的物质守恒，其中ϵ是螺距，r是距轴的距离。这种物质守恒性质使平衡可以简单地通过对螺旋流函数的限制来计算。这些状态通过它们的平均半径和质心位置进行参数化。在单个旋涡的情况下，我们的数值方法不能完全填充参数空间。我们猜测，在算法失败的地方，乘连通等高线将描述均衡。我们还考虑了围绕原点在方位上均匀分布的多个涡旋。利用螺旋CASL算法对稳定性进行了数值研究。
We present a family of steadily rotating equilibrium states consisting of helically symmetric vortices in an incompressible inviscid irrotational unbounded fluid. These vortices are described by contours bounding regions of uniform axial vorticity. Helical symmetry implies material conservation of axial vorticity (in the absolute frame of reference) when the flow field parallel to vortex lines is proportional to (1+ϵ2r2)−1/2, where ϵ is the pitch and r is the distance from the axis. This material conservation property enables equilibria to be calculated simply by a restriction on the helical stream function. The states are parameterized by their mean radius and centroid position. In the case of a single vortex, parameter space cannot be fully filled by our numerical approach. We conjecture multiply connected contours will characterize equilibria where the algorithm fails. We also consider multiple vortices, evenly azimuthally spaced about the origin. Stability properties are investigated numerically using a helical CASL algorithm.