[M-IS16] Geophysical fluid dynamics-Transfield approach to geoscience

[MIS16-04] Deformation of vortices on surfaces with domains of negative curvature

*Koki Ryono¹, Keiichi Ishioka¹ (1.Graduate School of Science, Kyoto University)

Keywords:two-dimensional fluid, filamentation, curvature, pattern formation

As a natural extension of the fluid dynamics on spheres considered in geophysical fluid dynamics, one can consider fluid dynamics on Riemann manifolds. In particular, when considering two-dimensional fluids subject to the Euler equation, it can be shown by differential geometrical calculations that the stretching of the fluid is influenced by the curvature. That is, in the region of positive curvature, the fluid stretching is decelerated and in the region of negative curvature, it is accelerated. Numerical integration of the time evolution of the vorticity field on a torus with a region of negative curvature confirms this effect. The relationship between vortex deformation and curvature is also discussed through simpler analytical examples.

Acceleration of vortex deformation is a phenomenon that also leads to filamentation of the vorticity field, the most elementary mixing process of two-dimensional fluids. Therefore, in this sense, it can also be related to the establishment of large-scale vortices characteristic of two-dimensional fluids. The talk will also provide an outlook on the application of vortex deformation effects due to negative curvature to the study of large-scale pattern formation in two-dimensional fluids.