x,y,t

Cartesian coordinates wherein x and y increase eastward and northward

〈 〈a,b〉 〉

Horizontal vector with eastward and northward components a and b

V=〈 〈u,v〉 〉

Horizontal velocity vector

∇≡〈 〈∂
_{
x
},∂
_{
y
}〉 〉

Horizontal gradient operator

p

Pressure

q≡v
_{
x
}−u
_{
y
}−y
p

Linearized Ertel’s potential vorticity: \(q^{*} \equiv v^{*}_{x^{*}}u^{*}_{y^{*}}  (f^{*}/{c^{*}}^{2}) p^{*}\)

φ
 Solution of ∇^{2}
φ−y
^{2}
φ−3φ
_{
tt
}=q, see (16) & (17a)

φ
^{app}
 Solution of ∇^{2}
φ
^{app}−y
^{2}
φ
^{app}=q, see (26a) & (18a)

(u
^{2}+v
^{2}+p
^{2})/2

Wave energy: (u
^{∗}
^{2}+v
^{∗}
^{2}+p
^{∗}
^{2}/c
^{∗}
^{2})/2

θ=k
x−ω
t

Wave phase

k

Zonal wavenumber

ω

Wave frequency

H
^{(n)}

Hermite polynomial, see endnote 1

n

Meridional mode number of free equatorial waves

\(\overline {A}\)

Phase average of A
