多涡自组织的初步研究

A PRELIMINARY STUDY ON THE SELF-ORGANIZATION PROCESS OF MULTI-VORTICES

在涡旋自组织动力学的框架内,用f平面二维准地转模式研究了初始场上不规则分布的由12个β和γ中尺度涡构成的涡群如何自组织成一个较大涡旋的问题。结果表明,多涡自组织是一个逐次合并的过程,开始时是相邻双涡的合并,然后形成三涡流型,最后才形成一个α中尺度的终态涡。因此,多涡共存条件下的双涡作用,是多涡自组织的一个基本的物理过程。初始场上的每一个涡或涡块,主要有两类“前景”,一是其涡量与相邻涡涡量合并,成为新的一个涡的内区的涡量来源;二是被相邻涡的环流拉伸,成为新的一个涡的螺旋带涡量的来源。每一个新的涡,类似地也有这两类前景,直至惟一的一个较大尺度的涡自组织起来。初始涡结构描述精度不同,自组织过程中涡互旋和涡合并的速率均会不同,终态涡内区涡量来源也不相同,说明准确给出初始涡群涡结构特征十分重要。最后指出了二维准地转流自组织过程数值解的一个属性,即总动能缓慢衰减,总涡度拟能迅速衰减,最大尺度涡旋的环流迅速加大。

In the context of advection dynamics, the self-organization process of initially scattered 12 meso-β and -γ scale vortices evolving into a synoptic-scale typhoon-like vortex is numerically explored with an f-plane 2-D quasi-geostrophic vorticity equation model in this paper. The results show that the self-organization process was a step-by-step merging course, namely the two adjacent vortices firstly merged, then tri-vortex flow pattern formed, and finally it evolved into a resultant vortex of meso-α scale. Thus it can be seen that the interaction of binary vortices under an ambient environment of multi-vortices coexistence was a basic physical process of multi-vortices self-organization. Each initial vortex or vorticity lump confronted two ways out ： it merged with an adjacent vortex, thus became a source of the inner region vorticity of the new formed vortex; or it was stretched by the circulation of a adjacent vortex, then became the vorticity source of the spiral band of the new vortex. Similarly, each new formed vortex also confronted the two ways out, until the multi-vortices self-organized into a single vortex of larger scale. The representation precision of the initial vortex structure directly affected the speeds of the mutual rotation and merging of binary vortices in the course of self-organization, and it also determined the source of the inner region vorticity of the resultant vortex. Therefore, it is important to provide the accurate description of initial vortices structure. At last, a property of the numerical solution of the self-organization for the 2-D quasi-geostrophic flow is that the total kinetic energy decays slowly, the total enstrophy decreases rapidly, and the circulation of the vortex of the largest scale grows quickly.