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首页> 外文期刊>Journal of Computational Physics >THE ONSET OF INSTABILITY IN EXACT VORTEX RINGS WITH SWIRL
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THE ONSET OF INSTABILITY IN EXACT VORTEX RINGS WITH SWIRL

机译：带旋流的精确涡旋环的不稳定性开始

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摘要

We study the time-dependent behavior of disturbances to in viscid vortex rings with swirl, using two different approaches. One is a linearized stability analysis for short wavelengths, and the other is direct flow simulation by a computational vortex method. We begin with vortex rings which are exact solutions of the Euler equations of inviscid, incompressible fluid flow, axisymmetric, and traveling along the axis; swirl refers to the component of velocity around the axis, Exact vortex rings with swirl can be computed reliably using a variational method. Quantitative predictions can then be made for the maximum growth rates of localized instabilities of small amplitude, using asymptotic analysis as in geometric optics. The predicted growth rates are compared with numerical solutions of the full, time-dependent Euler equations, starting with a small disturbance in an exact ring, These solutions are computed by a Lagrangian method, in which the three-dimensional flow is represented by a collection of vortex elements, moving according to their induced velocity. The computed growth rates are typically found to be about half of the predicted maximum, and the dependence on location and ring parameters qualitatively matches the predictions. The comparison of these two very different methods for estimating the growth of instabilities serves to check the realm of validity of each approach. (C) 1996 Academic Press, Inc. [References: 41]
机译：我们使用两种不同的方法研究了涡旋对粘性涡环的扰动随时间变化的行为。一种是针对短波长的线性化稳定性分析，另一种是通过计算涡流方法进行的直接流模拟。我们从涡环开始，这些环是无粘性，不可压缩流体流动，轴对称和沿轴行进的欧拉方程的精确解；旋涡是指绕轴速度的分量，可以使用变分方法可靠地计算出具有旋涡的精确涡旋环。然后，可以使用几何光学中的渐近分析，对小幅度局部不稳定性的最大增长率进行定量预测。从精确环中的小扰动开始，将预测的增长率与完整的，与时间相关的欧拉方程的数值解进行比较，这些解通过拉格朗日方法计算，其中三维流由一个集合表示涡元素的运动，根据它们的感应速度运动。通常发现计算出的增长率约为预测最大值的一半，并且对位置和环参数的依赖性在质量上与预测相符。将这两种截然不同的方法进行比较，以估计不稳定性的增长，可以检查每种方法的有效性。 （C）1996 Academic Press，Inc. [参考：41]

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