Table 2 List of symbols used in Section 2.1, where A is arbitrary quantities written dimensionally. The coordinate axes x, y, z increase eastward, northward, and vertically upward, respectively

f = f₀ + βy

Coriolis parameter

\( N=\sqrt{-\left(g/{\rho}_0\right)\left(d\overline{\rho}/ dz\right)} \)

Buoyancy frequency

x, y, z, t

Cartesian coordinates

〈〈a, b, c〉〉

Vector with x, y and z-axis components a, b, and c

U ≡ 〈〈u, v, w〉〉

Velocity vector

∇ ≡ 〈〈∂x, ∂y, ∂z〉〉

Gradient operator

Φ

Geopotential

q

Potential vorticity q ≡ v_x − u_y + [(f/N²)Φ_z]_z

φ

Solution of (6a)

φ^app

Solution of (7a)

\( \left(\overline{u^2+{v}^2+{\Phi}_z^2/{N}^2}\right)/2 \)

Wave energy density

μ = kx + mz − ωt

Wave phase

k

Zonal wavenumber

m

Vertical wavenumber

ω

Wave frequency

\( \overline{A} \)

Phase average of A