5 Buoyancy Forced Circulation and Cross-Gyre Flow
5.1 Introduction
This chapter discusses two subjects which appear at first sight unconnected, but
which in fact are linked by the underlying question of the way in which information is propagated in the dynamics of the ocean circulation.
The discussion in the previous chapters centers on fundamentally nondissipative dynamics in which, to the first approximation, the potential vorticity is carried unchanged along streamlines. It is natural then to think of the
determination of the potential vorticity, which is the key dynamical quantity in
the physics of the circulation, as being effected by the advection with the fluid
velocity. As the fluid moves, it does so along the path on which constant values
of the potential vorticity are inscribed. However, we have seen that this is not
the whole story when it comes to the flow of information in shaping the
structure of the circulation. The Sverdrup balance, with its integral along latitude circles, is a reflection of the purely westward propagation of barotropic
Rossby waves. Similarly, as we saw in Chapter 3, the shaping of the zones of
unventilated motion involves the interplay between advection by the fluid and
the westward propagation of baroclinic Ross by waves. Although the potential
vorticity equation is a hyperbolic system whose characteristics appear to be
given by the fluid velocity, the velocity itself is generally a complicated function
of the potential vorticity and its gradients. Therefore the direction of information flow in this mathematical system is not as simple as would obtain
were the potential vorticity equation of the more familiar, quasilinear type, i.e.,
with coefficients in which gradients of the potential vorticity do not appear.
The question of information flow is considerably more subtle. Information is
propagated simultaneously along streamlines as well as along latitude circles by
both barotropic and baroclinic Rossby waves.
If potential vorticity is not conserved, the flow paths and isolines of potential vorticity no longer coincide, and we can no longer associate each
streamline with a value of potential vorticity. We can then no longer find a first
integral of the potential vorticity equation, as in Chapter 4, where q = Q( ljJ, p).
Alternative formulations are necessary, and the issue of information flow becomes even more central to the physical discussion.
5.1 Introduction
This chapter discusses two subjects which appear at first sight unconnected, but
which in fact are linked by the underlying question of the way in which information is propagated in the dynamics of the ocean circulation.
The discussion in the previous chapters centers on fundamentally nondissipative dynamics in which, to the first approximation, the potential vorticity is carried unchanged along streamlines. It is natural then to think of the
determination of the potential vorticity, which is the key dynamical quantity in
the physics of the circulation, as being effected by the advection with the fluid
velocity. As the fluid moves, it does so along the path on which constant values
of the potential vorticity are inscribed. However, we have seen that this is not
the whole story when it comes to the flow of information in shaping the
structure of the circulation. The Sverdrup balance, with its integral along latitude circles, is a reflection of the purely westward propagation of barotropic
Rossby waves. Similarly, as we saw in Chapter 3, the shaping of the zones of
unventilated motion involves the interplay between advection by the fluid and
the westward propagation of baroclinic Ross by waves. Although the potential
vorticity equation is a hyperbolic system whose characteristics appear to be
given by the fluid velocity, the velocity itself is generally a complicated function
of the potential vorticity and its gradients. Therefore the direction of information flow in this mathematical system is not as simple as would obtain
were the potential vorticity equation of the more familiar, quasilinear type, i.e.,
with coefficients in which gradients of the potential vorticity do not appear.
The question of information flow is considerably more subtle. Information is
propagated simultaneously along streamlines as well as along latitude circles by
both barotropic and baroclinic Rossby waves.
If potential vorticity is not conserved, the flow paths and isolines of potential vorticity no longer coincide, and we can no longer associate each
streamline with a value of potential vorticity. We can then no longer find a first
integral of the potential vorticity equation, as in Chapter 4, where q = Q( ljJ, p).
Alternative formulations are necessary, and the issue of information flow becomes even more central to the physical discussion.