Ageostrophic instabilities in balanced, interior horizontal and vertical shear flows

The linear instabilities of several horizontal shear flows in a rotating shallow water model and several vertical shear flows in a stratified Boussinesq model are investigated. We focus on generic types of ageostrophic (unbalanced) instability in shear flows that are far from boundaries, and without equator, surface outcropping, or singular potential vorticity. The general ocean circulation, forced at planetary scales and strongly influenced by the rotation and stable stratification, are balanced in the sense that they are mostly geostrophic and hydrostatic in momentum. The classical barotropic and baroclinic instabilities generate geostrophic turbulence, but most of the energy is inhibited to transfer towards smaller scales due to the ``inverse cascade''. On the other hand, energy dissipation is only effective at very small scales. Therefore, a route to breakdown the balance is needed, in order that the energy is efficiently cascaded towards small scales. The planetary boundary layer, coast and bottom topographic regions are well known for the breakdown of balance and energy dissipation. When we pose the question of the breakdown of balance to the interior ocean, the ageostrophic instabilities become possible routes that lead to a forward energy cascade. Previous studied ageostrophic instabilities such as gravitational, Kelvin-Helmholtz, centrifugal, and frontal instabilities are either with unstable or weak stratification, beyond the control of the planetary rotation (with very large Rossby number), or special cases. We find that the ageostrophic instability is a generic behavior in interior shear flows and its occurrence does not require special “edges”. The mechanism and criterion of these ageostrophic instabilities will also be discussed.