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Vortex Dynamics and Scalar Transport in Rotating Stratified Turbulence-Construction of a ‘Vortex-Wave based Turbulence Model'-

旋转分层湍流中的涡动力学和标量输运-“基于涡流波的湍流模型”的构建-

基本信息

批准号：
15540365
负责人：
MIYAZAKI Takeshi
金额：
$ 2.3万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

9.1.A Hamiltonian moment model is constructed following a moment reduction procedure, in which each vortex is modeled by an ellipsoid of uniform potential vorticity, whose principal axes and inclination angles change under the influence of shear induced by other vortices. Direct numerical simulations based on the CASL-algorithm are performed in order to assess the validity of the model and to find out a clue to incorporate dissipative effects. The interaction of two co-rotating vortices on slightly different vertical levels is studied. The Hamiltonian moment model can predict the critical merger distance fairly well. Next, the interaction of counter-rotating vortex pair (dipole) is investigated. According to the ellipsoidal moment model, the inclination from the vertical axis approaches to π/2 and one of the principal axes of the ellipsoid grows exponentially with time, if two slender vortices are placed within a critical distance initially. The CASL-computation tells that the vortices … More keep the dipole structure quite robustly. They survive from tilting down by ejecting thin filaments from their top and bottom, even if they are placed very close.9-2.Refinements on the quasi-geostrophic wire-vortex model are proposed. We adapt the Gaussian integration method in the evaluation of the mutual energy integrals, instead of the moment approximation used in the previous wire model. The accuracy of integration is improved drastically even if two wire-vortices are placed very close. The refined model can circumvent the singular behavior of a counter rotating vortex pair, predicted by the previous wire moment model. We also introduce a realistic relation between the inclination angle and the vortex-slenderness parameter, assuming that each wire-vortex is a prolate spheroid. The latter refinement enables us to model fatter vortices more accurately.9-3.In order to show the presence of the chaotic motion around an ellipsoidal vortex analytically, we apply Melnikov's method to a weakly perturbed spheroidal vortex. The Melnikov functions computed along the heteroclinic and homoclinic orbits intersect zero transversely in any cases, suggesting the occurrence of chaotic mixing of fluid particles. In fact, numerically computed stroboscopic Poincare plots scatter near the heteroclinic and homoclinic orbits even when the perturbations are very weak. Less

9.1.哈密顿矩模型是按照矩简化程序构建的，其中每个涡旋都由均匀位涡的椭球体建模，其主轴和倾角在其他涡旋引起的剪切影响下发生变化。进行基于 CASL 算法的直接数值模拟，以评估模型的有效性并找出纳入耗散效应的线索。研究了垂直方向略有不同的两个同向旋转涡流的相互作用。哈密顿矩模型可以很好地预测临界合并距离。接下来，研究反向旋转涡旋对（偶极子）的相互作用。根据椭球矩模型，如果最初将两个细长涡旋放置在临界距离内，则与垂直轴的倾角接近π/2，并且椭球主轴之一随时间呈指数增长。 CASL 计算表明，涡流使偶极子结构保持相当稳健。即使它们放置得很近，它们也能通过从顶部和底部喷射细丝而避免向下倾斜。9-2.提出了对准地转线涡模型的改进。我们在互能积分的评估中采用高斯积分方法，而不是先前导线模型中使用的矩近似。即使两个线涡流非常接近，积分的准确性也会大大提高。改进后的模型可以规避先前线矩模型预测的反向旋转涡对的奇异行为。我们还引入了倾角和涡旋细长参数之间的现实关系，假设每个线涡旋都是长椭球体。后者的改进使我们能够更准确地模拟更胖的涡旋。9-3.为了分析地显示椭球涡旋周围混沌运动的存在，我们将梅尔尼科夫方法应用于弱扰动的球涡旋。在任何情况下，沿异宿和同宿轨道计算的梅尔尼科夫函数都横向相交于零，这表明流体粒子发生了混沌混合。事实上，即使扰动非常弱，数值计算的频闪庞加莱图也会散布在异宿和同宿轨道附近。较少的