884 
These equations may be expanded and rewritten 
du. d(wt+e ov oau 
= 20 
ap EB ( 2 ) (@- au) vein 
ox oy 
eee 
p 0x’ 
dv uto Ov Ou . 
a4 o( 5) )+u(2- ou) 4 200 sin ¢ 
yeaa 
p oy 
Equating the vorticity (dv/ox — du/dy) to 2 and 
writing u? + »y? = V?, we obtain 
Ou 
ane (Qwm + 20 sin ¢)v 
= + (Qn + 20 sin g)u = — 
lo 2; 
= eam (Dar ol Dy 
(9) 
19 noe 
ay (Oe le 
if we may assume that the density p is sensibly constant 
—an assumption which appears legitimate in the equa- 
torial region. 
Following Rossby [7], we shall call 2w the relative 
vorticity and (2w + 2 sin #) the absolute vorticity 
of the motion. Rossby [7, p. 71] has shown that after 
pressure has been eliminated the equations of motion 
reduce to 
£ Qe + 20sin 4) 
(10) 
+2), 
+ ay 
so that with the equation of continuity (@u/dx + 
dv/dy = 0) we obtain 
= —(2w + 20 sin ¢) ( 
4 @o + 20sin 4) = 0. (11) 
Therefore, 2m + 20 sin ¢ = k, where k is a constant 
along a trajectory but may differ from one trajectory 
to another. Writing & for (Qo + 20 sin ¢) and P for 
(p + $pV2) inequations (9) (P isthe dynamic pressure), 
we obtain 
a py = — 18 
at TS pas” 
(12) 
to) 
AT laa yee eae = 
at + ku nen 
The equations for steady streaming (0u/ot = dv/dt = 
0) reduce to 
—kv = — loP ' 
p 0x 
a (13) 
Go) 
ku = —=-—. 
p oy 
Equations (13) represent a pseudogeostrophic motion 
in which the streamlines are strictly parallel to the 
TROPICAL METEOROLOGY 
isobars of P and in which the space accelerations are 
allowed for, so that no further allowance need be made 
for the accelerations along the path or for the centrip- 
etal acceleration perpendicular to the path. Further- 
more, the equations are independent of variations in 
latitude, and the variations imposed upon the motion 
by the change of latitude are controlled by the con- 
stancy of the absolute vorticity along the streamlines. 
The constant k may vary from streamline to stream- 
line but will be constant along any particular stream- 
line; for practical purposes it may be regarded as con- 
stant between any pair of consecutive isobars (of P) 
regarded as streamlines. 
If we draw isobars of P at intervals of whole milli- 
bars, we can determine the value of k with an ordinary 
geostrophic wind scale at any point where a value of 
V is known. If we write 
= 2m + 20 sin ¢ (14) 
the value of ¢’ can be read from the scale as the value 
appropriate to the known value of V and the separa- 
tion of the isobars at the points. Since k is constant 
along the whole length of the stream ‘‘tube” enclosed 
by the particular pair of isobars, the value of relative 
vorticity 2w can be determined immediately from the 
equation, 
= 20 sin ¢’, 
2 = 20 (sin ¢’ — sin 4). (15) 
It is thus possible to identify the areas of cyclonic and 
anticyclonic vorticity when the motion is one of steady 
streaming and where values of P can be determined. 
Near the equator, where the geostrophic component 
of acceleration becomes small and the space accelera- 
tions become relatively more important, the advantage 
of explicitly eliminating changes in ¢ and in the space 
accelerations from the equations of motion is obvious. 
Practically, if time changes can be ignored, the advan- 
tage in using dynamic pressure is that the streamlines 
should be parallel to the isobars of P so that wind 
direction will indicate the direction of the isobars and 
vice versa, a facility so far denied to equatorial ana- 
lysts. 
The practical usefulness of this method depends on 
the feasibility (or possibility) of drawing the isobars 
of dynamic pressure P. Wind speeds are small in the 
equatorial region and so are pressure gradients, so that 
an accuracy in pressure reductions of at least a fifth 
of a millibar will be necessary if the method is to be 
tested. In British West Africa the altitudes of the sta- 
tions above sea level are not known with an accuracy 
sufficient to guarantee this, and attempts to verify the 
deductions in this area have had to be abandoned until 
the altitudes of the stations have been redetermined. 
It was stated earlier that the measured pressure 
gradients were much greater than previous theory de- 
manded. This difficulty may now be overcome by as- 
suming values of the relative vorticity near the equator 
greater than the ones Grimes assumed in his first cal- 
culations. 
So far we have discussed only cases of steady stream- 
ing, but one of the most important features of equa- 
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