Geography Reference
In-Depth Information
Fig. 7.12
Vertical section in a plane containing the wave vector k showing the phase relation-
ships among velocity, geopotential, and temperature fluctuations in an upward propagating
inertia-gravity wave with m<0,ν>0, and f>0 (Northern Hemisphere). Thin sloping
lines denote the surfaces of constant phase (perpendicular to the wave vector), and thick
arrows show the direction of phase propagation. Thin arrows show the perturbation zonal
and vertical velocity fields. Meridional wind perturbations are shown by arrows pointed
into the page (northward) and out of the page (southward). Note that the perturbation wind
vector turns clockwise (anticyclonically) with height. (After Andrews et al., 1987.)
distributions so that the flow tends to return toward geostrophic balance. This
section investigates the process by which geostrophic balance is achieved, that
is, the adjustment process. For simplicity we utilize the prototype shallow water
system; similar considerations apply to a continuously stratified atmosphere. For
linearized disturbances about a basic state of no motion with a constant Coriolis
parameter, f 0 , the horizontal momentum and continuity equations are
∂u
∂t
g ∂h
∂x
f 0 v =−
(7.69)
∂v
∂t +
g ∂h
∂y
f 0 u =−
(7.70)
H ∂u
∂h
∂t +
∂v
∂y
∂x +
=
0
(7.71)
where h
is again the deviation from the mean depth H . Taking ∂(7.69)/∂x
+
∂(7.70)/∂y yields
c 2 2 h
∂x 2
2 h
∂t 2
2 h
∂y 2
f 0 =
+
+
0
(7.72)
here c 2
gH and ζ =
∂v /∂x
∂u /∂y.
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