EQUATORIAL METEOROLOGY 
by a surge of the trade wind, however, the tongue of 
fresh air very often does not exceed 1500 m in thickness 
so that the frontal surface has a well-marked slope at 
the leading edge up to 1500 m but trails off horizon- 
tally behind. It is beyond the scope of this article to go 
into fuller detail in this matter of fronts; a complete 
account has been given by Forder [8]. 
THE EQUATIONS OF MOTION 
The equatorial region was defined earlier as the re- 
gion in which the Coriolis term in the equations of 
motion was no longer predominant in balancing the 
pressure term, so that although many of the problems 
of the equatorial zone are the same as those of the 
tropies generally, the particular problem of finding dy- 
namical equations applicable to the movements of air 
within the region is peculiar to the region. 
When one examines synoptic charts of the region, 
particularly during the northern summer, one is struck 
immediately by the remarkable uniformity in the speed 
and direction of the winds a little south of the equator 
and the great diversity of the winds, arising from the 
same air stream, after crossing the equator. Between 
5°S and 10°S in the Indian Ocean—Pacific area, for 
example, the winds are consistently from southeast to 
east, whereas north of the equator the winds may be 
from any direction from west through south to east. 
At the same time, the winds to the south are not very 
far from being geostrophic, whereas north of the equa- 
tor the winds are far from being geostrophic in most 
cases. 
Grimes [6] showed that it was possible to obtain in- 
tegrable equations of motion allowing for the variation 
of the Coriolis force with latitude, provided the con- 
ditions were very much simplified. The simplifications 
involved the assumption of steady horizontal motion 
with no friction and no variation in the motion with 
changing longitude. The further assumption that 
sin ¢@ = ¢ (¢ = latitude) was also made. Starting with 
an assumed value for the wind speed and direction at 
latitude 5°S and using Bjerknes’ circulation theorem, 
Grimes was able to compute the paths of the air across 
the equator and, from the same initial wind, to arrive 
at a variety of paths by simply changing the value of 
the assumed circulation of the air at latitude 5°S. It 
was also possible to compute the isobaric configuration 
that was necessary to maintain the motion, but the 
computed gradients of pressure were much smaller 
than the ones found in practice. The equations showed, 
too, that if an isobar crossed the equator, it must do 
so at right angles, but this was a consequence of the 
assumption of no variation with longitude and Crossley 
[1] pointed out that when this restriction was removed 
the necessity of an isobar’s crossing the equator at 
right angles disappeared. Crossley [2] has recently mod- 
ified Grimes’s treatment to obtain an exact solution 
using spherical polar coordinates instead of Cartesian 
coordinates. On the assumption that the motion is 
883 
steady and frictionless and that there is no change of 
velocity with longitude, the solution of the equations 
of motion becomes 
Uh = 
—20a cos ¢ + Bo + C, (1) 
v = A sec 4, (2) 
where ¢ is the latitude, \ is the longitude, a is the radius 
of earth, and A, B, and C are arbitrary constants. The 
streamlines are given by 
AX + 20a sin ¢ — 4B¢? — Co = const, (3) 
and the pressure distribution by 
a2 & AR + 4A tan? d + Qa[Qa cos 2¢ 
p 4 
+ 2B (sin ¢ — ¢ cos ¢) — 2C cos 4] + const. © 
The arbitrary constant A can be interpreted as the 
northward component of velocity at the equator. 
If we set B = O so that the pressure distribution is 
independent of longitude, we arrive at Grimes’s solu- 
tion in spherical polar form: 
u = C — 20a cos ¢, (5) 
v = A sec ¢. (6) 
The constant C is related to the assumed initial velocity 
and vorticity. 
Crossley goes on to say that if solutions of the Grimes 
type are found to exist, it follows that the gradient of 
pressure by itself is not sufficient to determine the 
horizontal motion of air in the tropics. In middle lati- 
tudes the assumption that the wind vanishes with the 
pressure gradient is in accord with experience, but this 
is not necessarily the case in the tropics. The theory 
indicates that once a motion across the isobars has 
come into existence on a large scale, this type of flow 
can continue in a similar fashion without any marked 
tendency to approximate the direction of the isobars 
unless higher latitudes are reached. It is clearly im- 
portant, as Crossley says, to determine how much 
cross-isobar motion exists in the free air and whether 
there is, in fact, any wind in the absence of a pressure 
gradient. 
Treloar [9] and Gibbs [5] have separately discussed 
the same problem, introducing the frictional effect but 
ignoring the space accelerations. Their treatment, how- 
ever, cannot be regarded as altogether satisfactory. 
Another method of approach to the problem may be 
suggested. The equations for frictionless horizontal mo- 
tion may be written 
CW 305) Sine sao 
dt p 0x 
d il @) @ 
v : Pp 
— PAO —— ke 
rr Qu sin d ai 
where all the symbols have their usual significance. 
