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6 Rotational Effects
is called the geostrophic method, being commonly used to derive the relative
geostrophic f ow fiel from measurements of density. See Pond and Pickard (1983)
for a detailed description of the geostrophic method.
For an ocean uniform in density, the geostrophic balance reads:
− f v geo = −g
∂η
∂ x
(6.12)
+ f u geo = −g
∂η
∂ y
(6.13)
The resultant geostrophic f ow runs along lines of constant pressure, provided by
sea-level elevations, and is independent of depth. Sea-level contours are therefore
the streamlines of surface geostrophic f ow. Such barotropic f ow cannot produce
much horizontal divergence and therefore tends to follow bathymetric contours
(see Cushman-Roisin (1994)). Inspection of bathymetry maps provides firs hints
on the likely path of geostrophic currents! The geostrophic circulation around a
low-pressure centre is referred to as cyclonic, whereas the circulation around a highpressure centre is called anticyclonic.
Horizontal divergence of geostrophic f ow is given by:
∂u geo
∂ x
+
∂v geo
∂ y
= −
β
f
v geo
(6.14)
where β is the meridional variation of the Coriolis parameter. This f ow
divergence/convergence occurs for equatorward or poleward f ow and it can be
typically ignored in regional studies on spatial scales <100 km. On larger scales,
however, fl w divergence associated with the beta effect is an important contributor
to the steady-state wind-driven circulation in the ocean, being discussed in Sect. 6.9.
6.4.4 Vorticity
Vorticity is the ability of a f ow to produce rotation. Imagine you throw a stick into
the sea. If this imaginary stick starts to spin around, there must be some non-zero
vorticity! A useful dynamical statement – conservation of potential vorticity – can
be derived from consideration of the equations governing the dynamics of depthindependent, nonfrictional horizontal fl ws given by:
∂u
∂t
+ u
∂u
∂ x
+ v
∂u
∂ y
− f v = −g
∂η
∂ x
(6.15)
∂v
∂t
+ u
∂v
∂ x
+ v
∂v
∂ y
+ f u = −g
∂η
∂ y
(6.16)
∂η
∂t
+
∂(uh)
∂ x
+
∂(vh)
∂ y
= 0
(6.17)