We have developed a momentum-based formulation of the extratropical circulation which exploits the interchangeability of momentum and temperature for quasi-balanced rotating stratified flow. This formulation makes explicit the role of the surface temperature gradient as a source of momentum, a result that is implicit, for instance, in an Eliassen-Palm formulation of the circulation.

The basic procedure is to rewrite the qg thermodynamic equation as a momentum equation. This introduces a new variable, called potential momentum, which is related to the thermal structure but has momentum units. The potential momentum is essentially the momentum distribution that gives the same contribution to the total PV as the baroclinic term in the original profile. Physically, it can also be interpreted as the zonal momentum that would be achieved by the flow if the mass of the isentropic layers was rearranged so as to make the isentropic thickness uniform poleward of a reference latitude. Based on this definition, easterly potential momentum is associated to isentropic layers that open up with latitude, as observed in the extratropical troposphere.

We extrapolate this definition to the surface using Bretherton's PV sheets. In this framework, a negative surface temperature gradient is equivalent to delta-function easterly potential momentum at the surface. We also derive the important constraint that the vertically integrated potential momentum (over some properly-defined mixing depth) must be constant. This implies that the reduction of the surface temperature gradient (i.e., of the potential momentum at the surface) must occur at the expense of the generation of an interior easterly potential momentum jet. This provides a link between the elimination of the surface temperature gradient and the development of a barotropic jet, as often found in idealized baroclinic life cycles.

An important advantage of this formulation is that when the total momentum (potential plus physical) is considered, the forcing by the residual circulation disappears and the only dynamical forcing of (total) momentum is the eddy PV flux. This PV flux must be balanced in equilibrium by the nonconservative forcing of (total) momentum, which includes a diabatic generation of potential momentum and a frictional forcing of physical momentum. This suggests that while the partition between potential and physical momentum can be forced remotely, the total momentum is determined locally through a forced-dissipative relation, much like in the 2D problem. The role of the residual circulation in this framework is to exchange potential and physical momentum so as to keep thermal wind balance.

We note that the conservation equation of total momentum is the y-integral of the qgpv equation. For symmetric 2D flow, momentum provides a full description and vorticity is redundant. Likewise, symmetric 3D flow can be encapsulated in terms of momentum alone, provided that we define a momentum expression of the baroclinic term (the potential momentum).

We conclude this presentation discussing some important advantages of this formulation, which shows some promise for a number of geophysical problems. In a different session of this meeting we will apply the formalism to the equilibration of an isolated baroclinic jet.