Abstract
Eddy saturation describes the nonlinear mechanism in geophysical flows whereby, when average conditions are considered, direct forcing of the zonal flow increases the eddy kinetic energy, while the energy associated with the zonal flow does not increase. Here, we present a minimal baroclinic model that exhibits complete eddy saturation. Starting from Phillips' classical quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we derive a reduced order model comprising of six ordinary differential equations including parameterised eddies. This model features two physically realisable steady state solutions, one a purely zonal flow and one where, additionally, finite eddy motions are present. As the baroclinic forcing in the form of diabatic heating is increased, the zonal solution loses stability and the eddy solution becomes attracting. After this bifurcation, the zonal components of the solution are independent of the baroclinic forcing, and the excess of heat in the low latitudes is efficiently transported northwards by finite eddies, in the spirit of baroclinic adjustment.
Highlights
The equilibrium volume transport of the Antarctic Circumpolar Current (ACC) is known to be balanced by three contributions, namely the input of momentum at the ocean surface by the wind, the downward transport of this momentum by eddies and the bottom drag as the opposite force to the wind (Munk and Palmen 1951; Nadeau and Ferrari 2015). Straub (1993) was first to suggest that the ACC volume transport is independent of the wind stress at the ocean surface the wind was assumed to be sufficiently strong
While mechanical stress dominates the oceanic processes described above, the baroclinic instability in the atmosphere is a result of the horizontal temperature gradient between the equator and poles, which is primarily due to the presence of a stronger radiative forcing at low rather high latitudes
At all levels of the atmosphere, the meridional temperature gradient is proportional to the vertical shear of the mean flow by thermal wind balance and is the source of available potential energy for the eddies which are associated with the storm tracks
Summary
The equilibrium volume transport of the Antarctic Circumpolar Current (ACC) is known to be balanced by three contributions, namely the input of momentum at the ocean surface by the wind, the downward transport of this momentum by eddies and the bottom drag as the opposite force to the wind (Munk and Palmen 1951; Nadeau and Ferrari 2015). Straub (1993) was first to suggest that the ACC volume transport is independent of the wind stress at the ocean surface the wind was assumed to be sufficiently strong. Pedlosky (1979); Hoskins and James (2014)), which focuses on studying the stability properties of the zonal flow, we use here methods of dynamical systems theory, which allow us to show the existence of a second attracting steady state instead of growing normal mode baroclinic instabilities. Another novel aspect is that this second steady state exhibits the above described eddy saturation properties in a model with parameterised eddies.
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