Geography Reference
In-Depth Information
occurs on the anticyclonic shear side of upper level jet streaks. The occurrence of
inertial instability over a large area would immediately trigger inertially unstable
motions, which would mix the fluid laterally just as convection mixes it verti-
cally, and reduce the shear until the absolute vorticity times f was again positive.
(This explains why anticyclonic shears cannot become arbitrarily large.) Inertial
instability is considered further in a more general context in Section 9.3.
7.5.2
Inertia-Gravity Waves
When the flow is both inertially and gravitationally stable, parcel displacements
are resisted by both rotation and buoyancy. The resulting oscillations are called
inertia-gravity waves
. The dispersion relation for such waves can be analyzed
using a variant of the parcel method applied in Section 7.4. We consider parcel
oscillations along a slantwise path in the (y, z) plane as shown in Fig. 7.11. For
a vertical displacement δz the buoyancy force component parallel to the slope of
the parcel oscillation is
N
2
δz cos α, and for a meridional displacement δy the
Coriolis (inertial) force component parallel to the slope of the parcel path is
−
f
2
δy sin α, where we have assumed that the geostrophic basic flow is constant in
latitude. Thus, the harmonic oscillator equation for the parcel (7.24) is modified
to the form
−
D
2
δs
Dt
2
(
f sin α
)
2
δs
(
N cos α
)
2
δs
=−
−
(7.55)
where δs is again the perturbation parcel displacement.
The frequency now satisfies the dispersion relationship
ν
2
N
2
cos
2
α
f
2
sin
2
α
=
+
(7.56)
Fig. 7.11
Parcel oscillation path in meridional plane for an inertia-gravity wave. See text for definition
of symbols.
