标题： 螺旋涡的运动 显示英文标题

标题： Motion of a helical vortex

摘要： 我们研究无限大、无粘性、不可压缩流体中单个螺旋涡的运动。该涡是一个无限管，其中心线为螺旋线，截面为小半径的圆（与曲率半径相比），其中涡度均匀且平行于中心线。自Joukowsky（1912）推导出该涡稳定地平移和旋转而不改变形状以来，已有大量尝试计算这些自诱导速度。在这里，我们使用Hardin（1982）对速度场的解，得到涡的线速度和角速度的新表达式。我们的结果通过数值计算Helmholtz积分和Biot-Savart定律的Rosenhead-Moore近似得到验证，在涡的螺距和截面的所有取值范围内都比之前的结果更准确。然后，我们使用新公式研究靠近涡的被动粒子的输运；我们发现涡的运动及其输送流体的能力取决于其螺距和截面如下：细长涡具有小螺距时移动速度快且携带少量流体；粗涡具有小螺距时以中间速度移动，自身是中等的携带者，但它沿螺旋轴向前推动流体；而具有大螺距的涡，无论细长还是粗大，移动缓慢且携带大量流体。 显示英文摘要

摘要： We study the motion of a single helical vortex in an unbounded, inviscid, incompressible fluid. The vortex is an infinite tube whose centerline is a helix and whose cross section is a circle of small radius (compared to the radius of curvature) where the vorticity is uniform and parallel to the centerline. Ever since Joukowsky (1912) deduced that this vortex translates and rotates steadily without change of form, numerous attempts have been made to compute these self-induced velocities. Here we use Hardin's (1982) solution for the velocity field to find new expressions for the vortex's linear and angular velocities. Our results, verified by numerically computing the Helmholtz integral and the Rosenhead-Moore approximation to the Biot-Savart law, are more accurate than previous results over the whole range of values of the vortex pitch and cross-section. We then use the new formulas to study the advection of passive particles near the vortex; we find that the vortex's motion and capacity to transport fluid depend on its pitch and cross section as follows: a thin vortex of small pitch moves fast and carries a small amount of fluid; a thick vortex of small pitch moves at intermediate velocities and is a moderate carrier itself but it pushes fluid forward along the helix axis; and a vortex of large pitch, whether thin or thick, moves slowly and carries a large amount of fluid.