Baroclinic Equilibration and the Maintenance of the Momentum Balance.Part I: A Barotropic Analog

Abstract

In this two-paper series the basic dynamics concerning the equilibration of a baroclinic jet are described, using as a reference the simple Charney?Boussinesq model. Though this problem has been studied in the past in more realistic configurations than considered here, this approach is novel. By describing the equilibration in terms of the eddy redistribution of momentum some insight is gained on the role of the momentum balance for thermal homogenization at the surface and, more generally, on why three-dimensionality is important for the equilibration of the baroclinic jet. Part I of this series introduces the basic formalism and provides a reference framework in which to understand the three-dimensional equilibration. A simple geometric constraint is derived that implies that there is a limit to the reduction of the negative potential vorticity (PV) gradient by short modes, and this constraint is shown to apply to the equilibration of the 2D problem. The maintenance of the momentum balance in the forced-dissipative case is also discussed. This is very simple for the 2D problem, as there is a local balance between the eddy forcing of momentum (the PV flux) and the nonconservative forcing. This implies that, when the PV fluxes are everywhere downgradient, there must be a negative (positive) PV gradient over those regions in which the mean flow acceleration is westerly (easterly).