The Motion of Air across the Equator

Abstract

A. Grimes once discussed the movement of air across the equator, assuming that the earth is flat and that the approximation sinφ=φ (φ=latitude) holds good.
The present author treats here the same problem without such assumtions. The equations of motion on the rotating earth are, in customary notations,
The above equations may be much simplified by making the assumptions such that the vertical velocity υ_r is nil, the motion is steady (∂/∂t=0) and zonal (∂/∂λ=0) and the air is incompressible; thus
Here the radius vector r is replaced by the radius of the earth a. The meridional component of velocity υθ is given by, from Eq. (3), and the longitudinal component of velooity υλ is derivable from Eq. (2):
Eq. (5) expresses the law of conservation of angular momentum and plays an important role in the veering of wind direction in traversing the equator.
In order to inspect the motion of air near the equator, θ₀ is taken as 95° (5°S) or 100° (10°S) and the motion towards the northern hemisphere is treated, therefore the first term in the righthand side of Eq. (5) is always negative in the neighbourhood of the equator. Thus, when υλ⁰ is negative (υλ⁰<0 means the easterly wind), the wind is easterly up to the latitude φ₀ (θ₀=90°+φ₀) in the northern hemisphere and then becomes westerly, while, when υλ⁰ is positive, two different cases occur according to the magnitude of υλ⁰. Namely, when υλ⁰ is small, the wind veers from westerly to easterly in the southern hemisphere and traverses the equator with easterly component, but soon tends to westerly over a certain latitude φ (φ<φ₀). When υλ⁰ is large, the wind maintains its westerly component and suffers no essential change across the equator. The above three types of track are given in Figs. 3_??_6.