How Do Hydrodynamic Instabilities Affect 3D Transport in Geophysical Vortices?

Abstract:

Understanding three-dimensional (3D) transport in ocean eddies is important for processes at a variety of scales, ranging from plankton production to climate variability. It is well known that geophysical vortices are subject to various hydrodynamic instabilities. Yet the influence of these instabilities on 3D material transport in vortex systems is not well investigated. Focusing on barotropic, inertial and 3D instabilities, we analyze these instabilities with normal-mode method, and reproduce their characteristics via highly-resolved numerical simulations using a spectral element Navier-Stokes solver. By comparing the simulation results of stable and unstable vortices, we investigate the joint impacts of instabilities on 3D transport through three major aspects: (i) energy transfer, (ii) overturning transport of the secondary circulation, and (iii) rates of vertical exchange and mixing. It is found that instabilities can enhance local nonlinear interactions and cause the kinetic energy wavenumber spectrum to have slopes between the conventional -5/3 and -3 at inertial ranges. The cascade of a new quantity is proposed to explain these non-conventional slopes. One of our main results is the discovery of material exchange between the central vortex and satellite vortices through 3D pathways, called funnels. These funnels modify the concept of elliptic regions that can trap material when confined to 2D dynamics. Thus, we show that a family of vortices, created by the hydrodynamic instabilities of the initially unstable vortex, can still continue to operate in unity in order to complete the 3D transport in these systems. We also show that flow instabilities can double the magnitude of vertical velocity, increase the rate of vertical exchange by an order of magnitude and enhance mixing rate more than 100%.