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

9.1.采用矩约化方法建立了一个哈密顿矩模型，其中每个涡都用一个均匀位涡椭球来模拟，其主轴和倾角在其他涡诱导的剪切的影响下发生变化。基于CASL算法的直接数值模拟进行，以评估模型的有效性，并找出一个线索，将耗散效应。研究了两个同向旋转涡在稍有不同的垂直高度上的相互作用。哈密顿矩模型能较好地预测临界合并距离。其次，研究了反向旋转涡对（偶极）的相互作用。根据椭球矩模型，当两个细长涡初始位置处于临界距离内时，椭球体相对于垂直轴的倾角接近π/2，且椭球体的一个主轴随时间呈指数增长。CASL计算表明， ...更多信息 保持偶极子结构相当坚固。它们通过从它们的顶部和底部喷射细丝而从倾斜中幸存下来，即使它们被放置得非常近。9 - 2.对准地转线涡模型提出了改进。我们适应高斯积分方法的相互能量积分的评价，而不是在以前的线模型中使用的矩近似。即使两个线涡非常接近，积分的精度也大大提高。改进后的模型可以避免由以前的线矩模型预测的反向旋转涡对的奇异行为。我们还介绍了一个现实的倾角和涡细长参数之间的关系，假设每个线涡是一个长椭球体。后一种改进使我们能够更精确地模拟较胖的旋涡。9 - 3.为了解析地显示椭球旋涡周围混沌运动的存在，我们将Melnikov方法应用于弱扰动的椭球旋涡。沿沿着异宿和同宿轨道计算的Melnikov函数在任何情况下都与零横向相交，表明流体粒子发生了混沌混合。事实上，数值计算的频闪庞加莱图分散在异宿和同宿轨道附近，即使扰动很弱。少

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