Equatorial Location

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To see why this is we need to examine the equations that govern motion in a longitudinally symmetric

atmosphere, equations (16)-(19):



Where u is zonal velocity, v is meridional velocity, w is vertical velocity Ω is the angular frequency of

the Earth's, ϕ is latitude, a is the radius of the Earth, ρ₀ normal background density, R is the

universal gas constant, H is the scale height of the atmosphere, and T is the temperature deviation.

Equation (16) shows that the longitudinal acceleration is balanced by some applied force F and the

Coriolis.

We can rewrite equations (16)-(19) into terms of u and F assuming solutions of waves, equation (20):


To become, equation (21):



We can look at the second term of the left hand side and do a scale analysis to see how it affects the

motion.

If we say that there is a height scale of D and a latitudinal scale of L then when get the

following relation to first order, equation (22).



This shows us that if L is very small (large) the second term in (21) becomes small (large) and the

acceleration (Coriolis force) is balanced the applied force.

Modern theory of the QBO uses 4 different waves: Kelvin, Rossby-gravity, inertia-gravity, and

gravity waves. These four give a rather good model of the observed QBO.

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