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

点击翻译按钮获取中文摘要

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