How do hydrodynamic instabilities affect 3D transport in geophysical vortices?

Three-dimensional (3D) transport within geophysical vortices (e.g.   ocean eddies) is important in understanding processes at a variety of scales, ranging from plankton production to climate variability. 3D transport can be affected by hydrodynamic instabilities of geophysical vortices; however, how the instabilities affecting 3D transport is not clear. Focusing on barotropic, inertial and 3D instabilities, we investigate the joint impacts of instabilities on 3D transport by using analytical methods and direct numerical simulations. We discover for the first time that material can be exchanged through 3D pathways which link a family of vortices generated by the instabilities in a single, initially unstable vortex. We also show that instabilities can increase the magnitude of vertical velocity, mixing rate and vertical material exchange. Besides, we find that instabilities can cause the kinetic energy wavenumber spectrum to have a power-law regime different than the classic regimes of k-5/3k-5/3 and k-3k-3, and propose a new energy spectrum to interpret the non-classic regime.