Fig. 8.

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Dispersion relation and eigenfunctions of the north-south ζz-symmetric columnar convective modes in the case of uniform rotation, no viscosity, and adiabatic stratification. (a) Dispersion relation of the north-south ζz-symmetric columnar convective modes in red points. For comparison, dispersion relation analytically derived using one-dimensional cylinder model by Glatzmaier & Gilman (1981) is overplotted in black dashed line. (b) Schematic illustration of flow structure of the mode. Red and blue volume rendering shows the structure of ℜ[ζz(r, θ)exp(imϕ − iωt)] for m = 6 at t = 0. (c) Meridional cuts of the m = 2 eigenfunctions for the velocity v(r, θ)exp[i(mϕ − ωt)], the pressure p1(r, θ)exp[i(mϕ − ωt)], and the z-vorticity ζr(r, θ)exp[i(mϕ − ωt)]. The solutions are shown in the meridional plane at ϕ = 0 and t = 0 where vr and vθ are purely real and vϕ, p1 and ζz are purely imaginary. The units of velocity, pressure, and vorticity are m s−1, 105 dyn cm−2, and 10−8 s−1, respectively. The eigenfunctions are normalized such that maximum of |vϕ| is 2 m s−1. (d) The same as panel c but for m = 8.
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