Geography Reference
In-Depth Information
the variation of the Coriolis parameter with latitude, the so-called β-effect. More
generally, in a baroclinic atmosphere, the Rossby wave is a potential vorticity-
conserving motion that owes its existence to the isentropic gradient of potential
vorticity.
Rossby wave propagation can be understood in a qualitative fashion by con-
sidering a closed chain of fluid parcels initially aligned along a circle of latitude.
Recall that the absolute vorticity η is given by η
=
ζ
+
f , where ζ is the relative
vorticity and f is the Coriolis parameter. Assume that ζ
0 at time t
0
. Now sup-
pose that at t
1
, δy is the meridional displacement of a fluid parcel from the original
latitude. Then at t
1
we have
=
(ζ
+
f )
t
1
=
f
t
0
or
ζ
t
1
=
f
t
0
−
f
t
1
=−
βδy
(7.87)
where β
df/dy is the planetary vorticity gradient at the original latitude.
From (7.87) it is evident that if the chain of parcels is subject to a sinusoidal
meridional displacement under absolute vorticity conservation, the resulting per-
turbation vorticity will be positive for a southward displacement and negative for
a northward displacement.
This perturbation vorticity field will induce a meridional velocity field, which
advects the chain of fluid parcels southward west of the vorticity maximum and
northward west of the vorticity minimum, as indicated in Fig. 7.14. Thus, the
fluid parcels oscillate back and forth about their equilibrium latitude, and the
pattern of vorticity maxima and minima propagates to the west. This westward
propagating vorticity field constitutes a Rossby wave. Just as a positive vertical
gradient of potential temperature resists vertical fluid displacements and provides
the restoring force for gravity waves, the meridional gradient of absolute vorticity
≡
Fig. 7.14
Perturbation vorticity field and induced velocity field (dashed arrows) for a meridionally
displaced chain of fluid parcels. Heavy wavy line shows original perturbation position; light
line shows westward displacement of the pattern due to advection by the induced velocity.
