The initial value problem for Kelvin vortex waves
The initial value problem for Kelvin vortex waves
复制标题
开尔文涡旋波的初值问题
DOI：
10.1017/s0022112097005958
复制
发表时间：
1997
影响因子：
3.7
通讯作者：
Ø. Andreassen
中科院分区：
文献类型：
--
作者：
S. Arendt;D. Fritts;Ø. Andreassen
本文给出了恒定涡量直涡管小扰动的初值问题的形式化解，并证明了对直涡管的任何初始扰动都只演变为开尔文涡波的集合。然后，我们详细研究了旋涡管的以下特定初始状态的演变：(i)管半径的轴对称夹紧，（ii）管位置的偏转，以及（iii）管横截面的平坦。所有这些初始状态都是通过高斯函数的加权在管道方向上定位的。在每一种情况下，初始扰动被分解成开尔文旋涡波包，然后沿着旋涡管向外传播。我们讨论了波包传播的物理机制，并研究了波色散对解决方案的影响。
We present a formal solution to the initial value problem for small perturbations of a straight vortex tube with constant vorticity, and show that any initial perturbation to such a tube evolves exclusively as a collection of Kelvin vortex waves. We then study in detail the evolution of the following particular initial states of the vortex tube: (i) an axisymmetric pinch in the radius of the tube, (ii) a deflection in the location of the tube, and (iii) a flattening of the tube's cross-secton. All of these initial states are localized in the direction along the tube by weighting them with a Gaussian function. In each case, the initial perturbation is decomposed into packets of Kelvin vortex waves which then propagate outward along the vortex tube. We discuss the physical mechanisms responsible for the propagation of the wave packets, and study the consequences of wave dispersion for the solution.