14
Sverdrup Theory
drives the flow in the mixed layer through the action of turbulent stresses. The
ocean beneath is set into motion by the purely inertial effects of vortex tube
stretching. The weak vertical velocity acting on the (relatively) large planetary
vorticity is the principal source of motion in the geostrophic region below the
mixed layer.
Generally the transport associated with the geostrophic portion of the
Sverdrup flow exceeds that due to the Ekman transport since their ratio is:
VG = o(curl(f/fJ))= o(L)=!!_ e
VE
fjj
fJL
L tan .
(1.3.13)
This ratio is normally greater than 1 since the length scale, L, associated with
the wind stress and the gyre scale is usually considerably smaller than the
earth's radius R. At 45°N, where tan(} is 1, the ratio is of the order of 6 if Lis
1000 km, and it is of order 3.5 at 30°N. In fact, in many cases theories for the
oceanic circulation focus entirely on the geostrophic portion of the transport.
This can lead to some confusion about the total mass balance if care is not
taken. In addition, the ratio in (1.3.13) reverses in magnitude for small(} as the
equator is approached. Indeed, a careful examination of (1.3.4) and (1.3.10)
shows that as the equator is approached VG---+- VE.
1.4 On the Validity of Sverdrup Theory
The elements of the Sverdrup theory, while limited to a description of only the
vertical integral of the motion field in the interior of the ocean, still form a
central building block of all the theories of the circulation that we discuss in
later chapters. It is therefore useful to examine more carefully the requirements
for its validity and the evidence for its correctness.
Sverdrup theory, as we have presented it, consists of two parts. There is
first the approximations leading to the Sverdrup vorticity balance, for example
(1.2.14) for the region below the mixed layer, and the Sverdrup balance
(1.2.16), for the vertically averaged meridional transport. The latter depends on
the former and the requirements for the Sverdrup balance are consequently
more severe. We examine each of these in tum.
First, let us consider the Sverdrup vorticity relation. As discussed in
Section 1.2, at least both the Rossby number and horizontal Ekman number
must be small, i.e.:
(1.4.la, b)
Sverdrup Theory
drives the flow in the mixed layer through the action of turbulent stresses. The
ocean beneath is set into motion by the purely inertial effects of vortex tube
stretching. The weak vertical velocity acting on the (relatively) large planetary
vorticity is the principal source of motion in the geostrophic region below the
mixed layer.
Generally the transport associated with the geostrophic portion of the
Sverdrup flow exceeds that due to the Ekman transport since their ratio is:
VG = o(curl(f/fJ))= o(L)=!!_ e
VE
fjj
fJL
L tan .
(1.3.13)
This ratio is normally greater than 1 since the length scale, L, associated with
the wind stress and the gyre scale is usually considerably smaller than the
earth's radius R. At 45°N, where tan(} is 1, the ratio is of the order of 6 if Lis
1000 km, and it is of order 3.5 at 30°N. In fact, in many cases theories for the
oceanic circulation focus entirely on the geostrophic portion of the transport.
This can lead to some confusion about the total mass balance if care is not
taken. In addition, the ratio in (1.3.13) reverses in magnitude for small(} as the
equator is approached. Indeed, a careful examination of (1.3.4) and (1.3.10)
shows that as the equator is approached VG---+- VE.
1.4 On the Validity of Sverdrup Theory
The elements of the Sverdrup theory, while limited to a description of only the
vertical integral of the motion field in the interior of the ocean, still form a
central building block of all the theories of the circulation that we discuss in
later chapters. It is therefore useful to examine more carefully the requirements
for its validity and the evidence for its correctness.
Sverdrup theory, as we have presented it, consists of two parts. There is
first the approximations leading to the Sverdrup vorticity balance, for example
(1.2.14) for the region below the mixed layer, and the Sverdrup balance
(1.2.16), for the vertically averaged meridional transport. The latter depends on
the former and the requirements for the Sverdrup balance are consequently
more severe. We examine each of these in tum.
First, let us consider the Sverdrup vorticity relation. As discussed in
Section 1.2, at least both the Rossby number and horizontal Ekman number
must be small, i.e.:
(1.4.la, b)