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 insta-bilities 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 À5=3 and k À3 , and propose a new energy spectrum to interpret the non-classic regime. The three-dimensional (3D) transport in geophysical vortices (e.g. ocean eddies) is crucial in understanding biological primary productions, air-sea gas exchanges, global tracer budgets, ocean general circulation, and thereby, climate variability (e.g. The 3D transport can be affected by hydrodynamic instabilities of geophysical vortices, such as barotropic and inertial instabilities; however, how these instabilities affecting the 3D transport is not clear. Barotropic instability in geophysical vortices has been extensively observed in laboratory experiments (e. instability receives well-known necessary conditions derived in inviscid parallel shear flows, including Rayleigh inflection-point criterion (Rayleigh, 1880), Rayleigh-Kuo inflection-point criterion (Kuo, 1949) and Fjørtoft's criterion (Fjørtoft, 1950). Centrifugal instability was explored in an inviscid swirling flow by Rayleigh (1917) who derived a necessary condition, known as Rayleigh circulation criterion. Later when studying inviscid flows between coaxial cylinders, Synge (1933) pointed out that the Ray-leigh circulation criterion is also a sufficient condition if perturbations are axisymmetric. When background rotation is considered, centrifugal instability is regarded as inertial instability. Inertial instability can form vertically-stacked overturning cells of selective scales (e. The Rayleigh circulation criterion is, however, invalid for non-axisymmetric perturbations, and still no general stability criterion is achieved (Drazin and Reid, 2004). Non-axisymmetric perturbations of swirling flows (or asymmetric perturbations of parallel flows) can draw energy from background flows and lead to non-ax-isymmetric inertial instability (or asymmetric inertial instability).