The Quasi-Geostrophic Circulation Problem
113
baroclinic Rossby wave speed, but the reader should keep in mind that this is
only a short-hand term for the more complex description of the speed required
to arrest the baroclinic wave on the interface by a flow limited to the upper
layers of the thermocline. The arresting flow is barotropic only with respect
within the upper two layers. It is baroclinic with respect to the full three-layer
model, and this is why the wave speed does not satisfy a simple Galilean
transformation.
3.5 The Quasi-Geostrophic Circulation Problem
Formulation
The heuristic analysis of the previous section shows that the nature of the
circulation, i.e., the distribution of the Sverdrup circulation among the density
layers of the ocean, may depend on the nature of the circulation itself. The
inability of the Rossby waves to breast the Sverdrup current reopens the
possibility that deeper layers, not directly forced by the Ekman pumping, are in
motion in regions shielded from Rossby wave arrivals from the eastern
boundary. These qualitative remarks, while illuminating, do not tell us with
any precision what these regions of deeper motion are and do not describe the
motion in those regions. The fact that the existence of such regions of deep
motion depends on the motion itself is a reflection of the fundamental
nonlinearity of the circulation problem, even in the interior where the Sverdrup
balance for the vertically averaged circulation is assumed to be valid. Indeed,
we discuss in the introduction to this chapter some of the perplexing and very
fundamental issues associated with developing a theory for the vertical
structure of the ocean circulation even if the Sverdrup balance is accepted for
the vertical average of the motion.
The attempts to develop a theory of the circulation of the upper ocean and
its vertical structure took a great step forward with the publication by Rhines
and Young of several important papers in the early years of the past decade
(Rhines and Young 1982a,b; Young and Rhines 1982). Employing the quasigeostrophic model, Rhines and Young were able to separate the problem for
the full vertical structure of the density field from the problem of determining
the vertical structure of the velocity field. Although the specification of the
basic density field means that the theory is only a partial theory for the full
vertical structure of the circulation, it illuminates very clearly the way in which
the circulation itself can shape its own structure through the nonlinear
interaction of the motion with the field of potential vorticity. As in the case of
the F ofonoff mode described in Chapter 2, the ability of the flow to reshape its
own potential vorticity isolines from latitude circles into curves which close on
themselves opens up new paths of allowable motion. For a baroclinic ocean
113
baroclinic Rossby wave speed, but the reader should keep in mind that this is
only a short-hand term for the more complex description of the speed required
to arrest the baroclinic wave on the interface by a flow limited to the upper
layers of the thermocline. The arresting flow is barotropic only with respect
within the upper two layers. It is baroclinic with respect to the full three-layer
model, and this is why the wave speed does not satisfy a simple Galilean
transformation.
3.5 The Quasi-Geostrophic Circulation Problem
Formulation
The heuristic analysis of the previous section shows that the nature of the
circulation, i.e., the distribution of the Sverdrup circulation among the density
layers of the ocean, may depend on the nature of the circulation itself. The
inability of the Rossby waves to breast the Sverdrup current reopens the
possibility that deeper layers, not directly forced by the Ekman pumping, are in
motion in regions shielded from Rossby wave arrivals from the eastern
boundary. These qualitative remarks, while illuminating, do not tell us with
any precision what these regions of deeper motion are and do not describe the
motion in those regions. The fact that the existence of such regions of deep
motion depends on the motion itself is a reflection of the fundamental
nonlinearity of the circulation problem, even in the interior where the Sverdrup
balance for the vertically averaged circulation is assumed to be valid. Indeed,
we discuss in the introduction to this chapter some of the perplexing and very
fundamental issues associated with developing a theory for the vertical
structure of the ocean circulation even if the Sverdrup balance is accepted for
the vertical average of the motion.
The attempts to develop a theory of the circulation of the upper ocean and
its vertical structure took a great step forward with the publication by Rhines
and Young of several important papers in the early years of the past decade
(Rhines and Young 1982a,b; Young and Rhines 1982). Employing the quasigeostrophic model, Rhines and Young were able to separate the problem for
the full vertical structure of the density field from the problem of determining
the vertical structure of the velocity field. Although the specification of the
basic density field means that the theory is only a partial theory for the full
vertical structure of the circulation, it illuminates very clearly the way in which
the circulation itself can shape its own structure through the nonlinear
interaction of the motion with the field of potential vorticity. As in the case of
the F ofonoff mode described in Chapter 2, the ability of the flow to reshape its
own potential vorticity isolines from latitude circles into curves which close on
themselves opens up new paths of allowable motion. For a baroclinic ocean